Symbolization Exercises From L2K

Logic 2000 Exercises Symbolization 2 © David Kaplan

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Symbolization Exercises from Logic 2000 Symbolization 2: Symbolization with AND, OR and BICONDITIONAL Symbolize each of the following sentences using the abbreviation scheme provided: 2.031 Ruth is tired, but she’ll pass.

P: Ruth will pass. S: Ruth studies. T: Ruth is tired

2.032 Either Ruth studies or she doesn’t pass. P: Ruth will pass. S: Ruth studies. T: Ruth is tired

2.033 Alfred does not study logic. S: Alfred studies logic

2.034 Although she's tired, Ruth will pass anyway. P: Ruth will pass. S: Ruth studies. T: Ruth is tired

2.035 Ruth will pass if, but only if, she studies. P: Ruth will pass. S: Ruth studies. T: Ruth is tired

2.036 Ruth is tired; nevertheless she’ll pass. P: Ruth will pass. S: Ruth studies. T: Ruth is tired

2.037 Ruth will pass just in case she studies. P: Ruth will pass. S: Ruth studies. T: Ruth is tired

2.038 Ruth studies only if she’s not tired. P: Ruth will pass. S: Ruth studies. T: Ruth is tired


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2.039 Either Alfred or Alonzo orders champagne.

R: Alfred orders champagne. Z: Alonzo orders champagne. T: Kurt orders champagne

2.040 Both Alfred and Alonzo order champagne.


2.041 Alfred is a lover of logic who organizes his time. R: Alfred is a lover of logic. T: Alfred organizes his time

2.042 Ruth is either a logician who enjoys chocolate or a mathematician who craves peanut butter.

P: Ruth is a logician. Q: Ruth enjoys chocolate. R: Ruth is a mathematician. S: Ruth craves peanut butter

2.043 If Alfred orders champagne, then so does Alonzo; and if Kurt orders champagne, then so does Alfred.


2.044 Ruth won’t pass unless she studies hard. P: Ruth will pass. S: Ruth studies hard. T: Ruth is tired

2.045 Mary will arrive at 10:30 am. unless the plane is late. R: Mary will arrive at 10:30a.m.. T: the plane is late

2.046 Neither Alfred nor Alonzo orders champagne. R: Alfred orders champagne. Z: Alonzo orders champagne. T: Kurt orders champagne

2.047 Alfred neither does well in the course nor loses track of the argument. W: Alfred does well in the course. T: Alfred loses track of the argument


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2.048 Ruth will pass if, but only if, she either studies hard or isn’t tired.

P: Ruth will pass. S: Ruth studies hard. T: Ruth is tired

2.049 If Ruth studies hard, then she’ll pass provided that she isn’t tired. P: Ruth will pass. S: Ruth studies hard. T: Ruth is tired

2.050 Either Ruth studies hard and will pass or she doesn’t (and won’t). P: Ruth will pass. S: Ruth studies hard. T: Ruth is tired

2.051 Either Alfred or Kurt, but not both Alonzo and Kurt, orders champagne. R: Alfred orders champagne. Z: Alonzo orders champagne. T: Kurt orders champagne

2.052 Both Alfred and Alonzo, but not Kurt, order champagne. R: Alfred orders champagne. Z: Alonzo orders champagne. T: Kurt orders champagne

2.053 If UCLA and USC don’t both win their first games, then USC and Cal both do win their first games.

U: UCLA wins its first game. S: USC wins its first game. Y: Cal wins its first game.

2.054 Ruth studies hard unless she’s tired, in which case she doesn’t.


2.055 Unless logic is difficult, Alfred will pass if he concentrates. P: Alfred will pass. Q: Alfred concentrates. R: logic is difficult. S: Alfred will secure employment. T: the text is readable. X: the lectures are exciting


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2.056 If UCLA wins its first game, then USC and Cal won’t both win their first games.

U: UCLA wins its first game. S: USC wins its first game. Y: Cal wins its first game

2.057 Assuming that either logic is difficult or the text is not readable, Alfred will pass only if he concentrates.

P: Alfred will pass. Q: Alfred concentrates. R: logic is difficult. S: Alfred will secure employment. T: the text is readable. X: the lectures are exciting

2.058 If neither Richard nor Tony will pass, Yiannis won’t either. R: Richard will pass. T: Tony will pass. Y: Yiannis will pass

2.059 If USC doesn’t win its first game, then both Cal and UCLA won’t win their first games. U: UCLA wins its first game. S: USC wins its first game. Y: Cal wins its first game

2.060 If either Tony or Yiannis will pass, then so will Richard unless he is tired. R: Richard will pass. T: Tony will pass. Y: Yiannis will pass. U: Richard is tired.

2.061 Either Cal wins its first game and UCLA does not win its first game or if UCLA wins its

first game then USC does not win its first game. U: UCLA wins its first game. S: USC wins its first game. Y: Cal wins its first game

2.062 Yiannis and Tony will definitely pass; Richard however, will fail if he doesn’t study (and, for that matter, will fail even if he does).

R: Richard will pass. T: Tony will pass. Y: Yiannis will pass. V: Richard will study. X: Richard will fail


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2.063 If Ruth will pass so long as she isn’t tired, then she’ll surely pass if she studies hard.


2.064 USC wins its first game provided that UCLA does not win its first game, but USC wins its first game only if Cal wins its first game.


2.065 Either it is not the case that Richard pays attention and does not lose track of the argument, or it is not the case that he does not take notes or fails to do well in the course.

P: Richard pays attention. S: Richard loses track of the argument. T: Richard takes notes. W: Richard does well in the course

2.066 Given that Cal wins its first game, USC does not win its first game provided that UCLA wins its first game.


2.067-2.070 use the following abbreviation scheme:

P: Rudolf’s prayers are answered. V: Rudolf believes in God. X: God exists. W: this is the best of all possible worlds. T: everything is permitted

2.067 If Rudolf’s prayers are answered if he believes in God, then God exists.

2.068 Rudolf does not believe in God unless this is the best of all possible worlds.

2.069 This is not the best of all possible worlds.

2.070 If God does not exist, then everything is permitted.


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2.071 Symb 2.071: Neither UCLA nor USC will win its first game unless both are willing to

work harder. U: UCLA wins its first game. S: USC wins its first game. Y: Cal wins its first game. W: UCLA is willing to work harder. R: USC willing to work harder

2.072 Symb 2.072: They (Richard, Tony, and Yiannis) won’t all pass.

R: Richard will pass. T: Tony will pass. Y: Yiannis will pass

2.073 Symb 2.073: Richard won’t pass, but at least one of the other two (Tony and Yiannis) will.


2.074 Symb 2.076: Unless either neither Sy nor Nye neigh or Bob and Babs both bray, none of them will beat Whirlaway.

P: Sy neighs. Q: Nye neighs. R: Bob brays. S: Babs brays. T: Sy will beat Whirlaway. U: Nye will beat Whirlaway. V: Bob will beat Whirlaway. W: Babs will beat Whirlaway

2.077 Symb 2.077: Sherlock Holmes will neither play his violin nor ask Watson for the needle; nevertheless, neither he nor Watson will fail to be baffled by Moriarty.

P: Sherlock Holmes will play his violin. Q: Sherlock Holmes will ask Watson for the needle. R: Sherlock Holmes will be baffled by Moriarty. S: Watson will be baffled by Moriarty

2.078 Symb 2.078: Although Richard will be disappointed unless the critics approve, the concert will be worthwhile if and only if the music is played well.

P: Richard will be disappointed. R: the critics approve. T: the concert will be worthwhile. W: the music is played well


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2.079 Symb 2.079: Neither Donald nor Richard is eager, but each is willing if the other is.

R: Donald is eager. S: Richard is eager. W: Donald is willing. X: Richard is willing

2.080 Symb 2.080: C.C. will pass unless the test is both too long and too hard, provided that the instructor is neither biased nor perverse.

P: C.C. will pass. T: the test is too long. R: the test is too hard. U: the instructor is biased. V: the instructor is perverse

2.081 Symb 2.081: If C.C. studies logic, then he does not do well in the course only if he does not take notes and pay attention.

X: C.C. studies logic. P: C.C. pays attention. S: C.C. loses track of the argument. T: C.C. takes notes. W: C.C. does well in the course

2.082-2.085 use the following abbreviation scheme:

V: Donald is a lover of logic. R: Donald organizes his time. W: Donald enjoys whiskey at night. Z: Donald enjoys Mozart in the morning

2.082 Donald is a lover of logic only if he does not organize his time. 2.083 Donald enjoys whiskey at night provided that he both enjoys Mozart in the morning and

organizes his time. 2.084 If Donald is a lover of logic who organizes his time, then he enjoys Mozart in the

morning or whiskey at night, but not both. 2.085 If Donald enjoys whiskey at night, then either he enjoys Mozart in the morning and

organizes his time, or he does not enjoy Mozart in the morning and does not organize his time, or else he is not a lover of logic.


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2.086 Symb 2.086: Assuming that the professor is a Communist, he will sign the loyalty oath;

but if he is an idealist, he will neither sign the loyalty oath nor speak to those who do. P: the professor is a Communist. S: the professor will sign the loyalty oath. T: the professor is an idealist. Y: the professor will speak to those who do sign the loyalty oath

2.087 Symb 2.087: Errors will decrease in the subject’s performance just in case neither motivation is absent nor learning has not occurred.

R: Errors will decrease in the subject’s performance. T: motivation is absent. U: learning has occurred

2.088 Symb 2.088: If Bertie and Hans are playing dice together, it is the first throw of the game,

and Bertie is throwing the dice, then he wins the game on the first throw if and only if he throws 7 or 11.

P: Bertie is playing dice. Q: Hans is playing dice. R: Bertie and Hans are playing dice together. S: it is the first throw of the game. T: Bertie is throwing the dice. U: Bertie wins the game on the first throw. V: Bertie throws 7. W: Bertie throws 11

2.089 Symb 2.089: If the world is a progressively realized community of interpretation, then either quadruplicity drinks procrastination or, provided that the Nothing negates, boredom will ensue seldom more often than frequently.

W: the world is a progressively realized community of interpretation. Q: quadruplicity drinks procrastination. X: the Nothing negates. R: boredom will ensue seldom more often than frequently

2.090 Symb 2.090: Errors will occur in the subject’s performance if and only if motivation is absent or learning has not taken place.[Ambiguous]

R: Errors will occur in the subject’s performance. T: motivation is absent. U: learning has occurred

2.092 Symb 2.092: Neither Bertie nor Hans will listen except when the other is speaking. P: Bertie will listen. Q: Hans will listen. R: Bertie is speaking. S: Hans is speaking


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2.093 Symb 2.093: No more than one of then (Richard, Tony, and Yiannis, of course) will pass. R: Richard will pass. T: Tony will pass. Y: Yiannis will pass

2.094 Symb 2.094: Exactly two of then (among Richard, Tony, and Yiannis) will pass.


The rest use the following abbreviation scheme:

P: Paula will pass. Q: Quincy will pass. R: Rachel will pass. S: Sidney will pass. T: Paula is tired. U: Quincy studies hard. V: Rachel studies hard. W: Paula studies hard. X: Sidney studies hard. Y: Quincy is tired

2.100 Paula, who studies hard, will pass.

2.101 Paula won’t pass unless she studies hard.

2.102 Paula neither studies hard nor passes.

2.103 Paula will pass if, but only if, she either studies hard or isn’t tired.

2.104 Either Paula studies hard and will pass or she doesn’t (and won’t).

2.105 If Paula will pass unless she’s tired, then she’ll pass so long as she studies hard.

2.106 Although she’s tired, Paula will pass anyway.

2.107 Provided that Paula studies hard, she’ll pass just in case she isn’t tired.

2.108 Paula studies hard unless she’s tired, in which case (that is, if she’s tired) she doesn’t.

2.109 If either Quincy or Rachel will pass, then so will Paula unless she is tired.

2.110 Paula and Quincy study hard and will pass.

2.111 Unless neither Paula nor Quincy studies hard, both will pass.

2.112 Both Paula and Quincy won’t pass, but Rachel and Sidney won’t fail to pass.


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2.113 Paula will pass just in case neither Quincy nor Rachel doesn’t study hard.

2.114 If and only if Paula is not tired, will she and Rachel pass.

2.115 Unless she studies hard, Paula will study hard and pass just in case Quincy does the same.

2.116 Quincy studies hard, but Rachel studies hard and passes.

2.117 Either Sidney will pass without studying hard, or on the condition that Quincy both studies hard and passes, Sidney will fail to pass.

2.118 Quincy, who studies hard, also will pass, unless Sidney will fail to pass only on the condition that he fails to study hard.

2.119 Paula will neither study hard nor pass, but either Rachel or Quincy, but not Sidney, will pass.

2.120 Although Paula isn’t tired, she neither studies hard nor passes; but Sidney won’t study hard and won’t pass.

2.121 Unless Rachel, who either failed to study hard or succeeded in passing, does pass, Sidney will neither study hard nor fail to study hard.

2.122 Quincy will either study hard or fail to pass, but not both; hover, Rachel studies hard just in case it is not the case that she will pass ii and only if it is the case that she will pass.

2.123 Paula neither studies hard, nor is tired, nor passes, but Quincy does all three.

Logic 2000 Exercises Symbolizations © David Kaplan

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Symbolization Exercises from Logic 2000 Symbolization 3: Symbolizations with one-place predicates Symbolize each of the following sentences using the abbreviation scheme provided: F1: a is good. G1: a is edible. H1: a is a sweet. I1: a is a chocolate. J1: a is healthy. K1: a should be enjoyed. L1: a poisoned my friend 3.001: Everything is good.

3.002: Nothing is good.

3.003: Something is good.

3.004: Something is not good.

3.005: All sweets are good.

3.006: No sweets are good.

3.007: Some sweets are good.

3.008: Some sweets are not good.

3.009: Only chocolates are good.

3.010: All and only sweets are edible.

3.011: All sweet things and edible things are good.

3.012: Among sweets, only chocolates are healthy.

3.013: Chocolates that are good should be enjoyed.

3.014: Chocolates, which are good, should be enjoyed.

3.015: A chocolate should be enjoyed.

3.016: A chocolate poisoned my friend.

3.017: Nothing other than a chocolate is good.

3.018: Only chocolates are good.


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3.030: Something is round and something is square, but it is not the case that something is a round square.

F1: a is round. G1: a is square 3.031: If everything is mental, then nothing is physical unless something is both mental and

physical. F1: a is mental. G1: a is physical 3.032: None but the brave deserve the fair. F1 : a is brave. G1 : a deserves the fair 3.033: Kettles boil quickly only if not watched. F1: a is a kettle. G1 : a boils quickly. H1 : a is watched 3.034: Kettles boil quickly if not watched. F1: a is a kettle. G1 : a boils quickly. H1: a is watched 3.035: Some soldiers love war, but not all who love war are soldiers. F1: 1 is a soldier. G1: a loves war 3.040: Among equine mammals, all and only zebras have dark stripes on a white or buffy

background. F1: a is an equine mammal. G1: a a is a zebra. H1 : a has dark stripes on a white or buffy background 3.041: Democrats an d Republicans who put loyalty above legality are detrimental to

democracy. F1: a is a Democrat G1: a is a Republican. H1 : a puts loyalty above legality. J1: a is detrimental to democracy 3.042: Professors are good lecturers if and only if they are both witty and intellectually

competent F1: a is a professor. G1 : a is a good lecturer. H1 : a is witty. J1: a is intellectually competent


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3.043: If a registered voter has not declared a party and only those who have declared a party can vote in a primary election, then he or she cannot vote in a primary election.

F1: a is a registered voter. G1: a has declared a party. H1: a can vote in a primary election 3.044: If only Republicans support the incumbent and no Democrat supports the candidate, then

if anyone is a Democrat, someone supports neither the incumbent nor the candidate. F1: a is a Republican. G1 : a supports the incumbent H1: a is a Democrat J1 : a support the candidate 3.045: If those who believe in God have immortal souls, then, given that God exists, they will

have eternal bliss. F1: a believes in God. G1: a has an immortal soul. H1: a will have eternal bliss. P: God exists 3.050: Only policemen and firemen are both indispensable and underpaid. F1: a is a policeman. G1: a is a fireman. H1 : a is indispensable. J1 : a is underpaid 3.051: All fruits and vegetables are wholesome and nourishing. F1: a is a fruit. G1 : a is a vegetable. H1 : a is wholesome. J1 : a is nourishing F1: a is a doctor. G1 : a is a lawyer. H1: a is rich. J1: a is admired. K1 : a is honest 3.052: Doctors and lawyers who are rich are admired only if they're also honest 3.053: Doctors and lawyers, who are rich, are admired only if they're also honest. F1: a reads The Daily Bruin in class. G1 : a is inconsiderate. H1: a is illiterate 3.097: Those who read The Daily Bruin in class are inconsiderate, but none of them are illiterate. 3.098: If there is no one who does not read The Daily Bruin in class, then only the inconsiderate

are literate. 3.099: If any woman studies, then no student passes unless she does. F1 : a is a woman. G1: a studies. H1: a is a student. J1: a passes


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F1: a jumps. I1: a is a dog. L1: a is yellow. G1: a sings. J1: a is a canary. M1: a is long-haired. H1: a is petted. K1 : a is a dolphin. N1 : a is a pet. A: Spot B: Kiwi. C: Feathers 3.201: Dogs and dolphins jump if petted.

3.202: Only dogs and dolphins jump if petted.

3.203: Dogs and dolphins jump only if petted.

3.204: Dogs and dolphins jump only if Spot and Kiwi are petted.

3.205: No pet neither sings no r jumps..

3.206: Some dogs both sing and jump, but only long-haired dogs are petted.

3.207: If a pet is yellow, then it sings but doesn't jump.

3.208: If Feathers sings and all who sing jump, then Feathers will not fail to jump.

3.209: Given that all pets jump or sing and no canary jumps, no canary is a pet unless it sings.

3.210: No dolphin sings unless it jumps.

3.211: No dolphin sings unless Kiwi jumps.

3.212: If a dolphin is petted, it will jump.

3.213: If all dolphins are petted, they will all jump.

3.214: A dolphin jumps.

3.215: Only a dog is long-haired.

3.216: Unless Spot is a canary, he neither sings nor is yellow.

3.217: Both Spot and Kiwi jump, but only if they are pets are they petted.

3.701: If a cancer survivor wins the Tour de France, then he's a superb athlete or on drugs. F1: a is a cancer survivor. G1: a wins the Tour de France. H1: a is a superb athlete. I1: a is on drugs 3.702: Men and women who enjoy martinis sleep well M1: a is a man. O1: a is a woman. J1: a enjoys martinis. K1: a sleeps well 3.703: Only logicians and mathematicians like quantifiers F1: a likes quantifiers. G1: a is a logician. H1: a is a mathematician 3.704: Among adults, only husbands and wives are excluded from singles clubs F1: a is an adult. J1: a is excluded from singles clubs. H1: a is a husband. G1: a is a wife


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3.705: No smoker is in jeopardy unless he or she inhales M1: a is a smoker. J1: a is in jeopardy. H1: a inhales F1: a is friendly. G1: a is mean H1: a is an elf. I1: a will bite. J1: a is provoked. B: Bruce. C: Carrie 3.706: If all elves are mean, no elf won't bite. 3.707: All elves who are mean will bite. 3.708: Although some mean elves will bite even though not provoked, neither Bruce nor Carrie

will bite unless provoked. 3.709: Given that some mean elf will bite and some friendly one will too, the mean ones will bite

whether or not provoked but the friendly ones will bite only if provoked. 3.710: No Republican is in the majority unless only Republicans are in the majority. F1: a is a Republican. G1: a is in the majority 3.711: Neither Republicans nor Democrats are honest except when it benefits them F1: a is a Republican. G1: a is a Democrat H1: a is honest I1: Being honest benefits a


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Symbolization 4: Symbolizations with two- and three-place predicates Symbolize each of the following sentences using the abbreviation scheme provided: F1: a is a person. G2: a loves b 4.001 Everyone loves someone. (Ambiguous – symbolize two non-equivalent ways.)

4.002 Someone loves someone.

4.003 If anything is a person, then someone loves him or her self.

4.004 Someone loves everyone. (Ambiguous – symbolize two non-equivalent ways.)

4.005 Everyone loves everyone.

F1: a is a student. G1: a is a teacher. H1: a is a subject. S3: a studies b with c 4.006 Every student studies every subject with every teacher.

4.007 Every student studies some subject with some teacher.

4.008 No student studies every subject with a teacher.

4.009 No student studies every subject with the same teacher.

4.010 Only students study every subject with a teacher.

4.011 No subject is such that every student studies it with every teacher.

4.012 No subject is such that every student studies it with the same teacher.

4.013 Every teacher has some subject that some student studies with him or her.

4.014 Each subject has some student who studies it with some teacher.

4.015 None but teachers are such that all students study all subjects with them.

4.016 Anyone who studies any subject with any teacher is a student.

4.017 There is a teacher such that every student studies some subject with him or her.

4.018 There is a teacher such that some student studies every subject with him or her.

4.019 Teachers who study some subject with a teacher are students.

4.020 No student who does not study every subject with a teacher is a teacher.

4.021 Any student who studies any subject with himself or herself is a teacher.

4.022 Some teacher who studies every subject with himself or herself is a student.

4.023 There is no teacher with whom any student studies all subjects.


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4.024 Every husband and wife has a spouse. F1: a is a husband. G1: a is a wife. H2: a is a spouse of b 4.025 No one lacks a father, but not everyone is a father. F1: a is a person. G2: a is a father of b 4.026 Every number has some number as its successor. F1: a is a number. G2: a is a successor of b 4.027 Some number is a successor of every number. F1: a is a number. G2: a is a successor of b 4.028 A teacher has no scruples if he or she assigns a problem that has no solution. F1: a is a teacher. G1: a has scruples. H2: a assigns b. J1: a is a problem. K2: a is a solution of b 4.029 No principle is innate unless everyone who hears it assents to it. F1: a is a principle. G1: a is inate. H1: a is a person. J2: a hears b K2: a assents to b 4.030 The cube of the square of 2 is even. F1: a is even. a1: the cube of a. b1: the square of a. c1: 2 4.031 No monk likes every course he takes unless the only courses he takes are theological

studies. F1: a is a monk. G1: a is a course. H1: a is a theological study. J2: a takes b. K2: a likes b 4.032 A man who loves himself more than he loves anyone else is not loved by anyone other

than himself. F1: a is a man. G1: a is a person. H2: a loves b. J2: a is different from b. L4: a loves b more than c loves d 4.033 If a father has only male children, then he does not have to provide a dowry for any

one of them. F1: a is a father. G1: a is a male. H2: a is a child of b. J2: a has to provide a dowry for b. L4: a loves b more than c loves d 4.034 Alfred is a friend of those who have no friends. F2: a is a friend of b. a: Alfred


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Some of the following cannot be done until after our unit 6 – they are marked in bold. 4.035 The spouse of anyone who marries the child of the brother of his or her father marries

the child of the brother of the spouse of his or her mother. F2: a marries b. a1:the spouse of a. b1:the child of a. c1: the brother of a. d1: the father of a. e1: the mother of a 4.036 Every husband and wife has a spouse. F2: a is a spouse of b. G1: a is a husband. H1: a is a wife 4.037 If x is an integer greater than or equal to zero and every integer is divisible by x, then

x is equal to 1. F1: a is an integer. G2: a is greater then b. H2: a is equal to b. I2: a is divisible by b. a: zero. b: 1 4.038 No one lacks a father, but not everyone is a father. F2: a is a father of b. G1: a is a person 4.039 The square of the length of the hypotenuse of a right triangle is equal to the sum of the

squares of the lengths of the other two sides. F1: a is a right triangle. G2: a is a side of b. H2: a is equal to b. J2: a is different from b. a1: the square of a. b1: the hypotenuse of a. c2: the sum of a and b. d1: the length of a 4.040 Someone is hit by a car every day. (Ambiguous – symbolize 5 non-equivalent ways.) F1: a is a person. G1: a is a car. H1: a is a day. J3: a is hit by b on c 4.041 You can fool some of the people all of the time. (Ambiguous – symbolize 2 non-

equivalent ways.) F2: you can fool a at b. G1: a is a person. H1: a is a time. 4.042 You cannot fool all of the people all of the time. F2: you can fool a at b. G1: a is a person. H1: a is a time. 4.043 The product of 3 and the square of 6 plus 3 is even. (Ambiguous – symbolize 3 non-

equivalent ways.) a: 3 b: 6. c2: a plus b. d2: the product of a and b. e1:the square of a. F1: a is even.


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Symbolization Exercises from Logic 2000 Symbolization 5: Symbolizations with Identity and Operation Letters Symb 5.001: Something differs from everything except itself.

Symb 5.002: Everything is identical with something.

Symb 5.003: Everything is distinct from something.

Symb 5.004: Everything equal to a thing differs from everything not equal to that thing.

Symb 5.005: Nothing differs from everything.

Symb 5.006: Things equal to the same thing are equal to each other.

Symb 5.007: Nothing differs from itself Symb 5.008: None but Alfred and his teacher are able to solve the problem. F2: a is able to solve b. a: Alfred. b: the problem. c1: the teacher of a Symb 5.009: Alfred attended the conference and arrived at it before everyone else who

attended it except Mary. F2: a attended b. G3: a arrived at b before c. a: Alfred. b: the conference. c:

Mary Symb 5.010: Alfred is the only member of the class who can read Greek. F2: a is a member of b. G2: a can read b. a: Alfred. b: the class. c: Greek Symb 5.011: Greensleeves can jump farther than any other frog in Calaveras County. F2: a can jump farther than b. G1: a is a frog. H2: a is in b. a: Greensleeves. b: Calaveras County Symb 5.012: Pergolesi was the most promising composer of his time. F2: a was more promising than b. G1: a was a composer. H2: a was contemporary with

b. a: Pergolesi Symb 5.013: Anyone whose mother is the wife of a citizen, whose father is married to his or

her mother, and whose father has no other children is the child of a citizen. F1: a is a citizen. G2: a is married to b. H2: a is a child of b. a1: the mother of a. b1: the wife of a. c1: the father of a. d1: the child of a Symb 5.014: If the sister of Alfred is the wife of the brother-in-law of Alfred, then the father-

in-law of Alfred is the father-in-law of the sister of Alfred. a: Alfred. b1: the wife of a. c1: the sister of a. d1: the brother-in-law of a. e1: the father-in-law of a Symb 5.015: If a sister of Alfred is the wife of a brother-in-law of Alfred, then the father-in-law

of Alfred is the father-in-law of a sister of Alfred.


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a: Alfred. b1: the wife of a. c1: the father-in-law of a. F2: a is a sister of b. G2: a is a brother-in-law of b. Symb 5.016: If a sister of Alfred is the wife of a brother-in-law of Alfred, then the father-in-law

of Alfred is the father-in-law of that sister of Alfred. a: Alfred. b1: the wife of a. c1: the father-in-law of a. F2: a is a sister of b. G2: a is a brother-in-law of b. Symb 5.017: Brothers and sisters I have none, but that man's father is my father's son. a: the speaker. b: that man. c1: the father of a. d1: the son of a. F2: a is a

brother of b. G2: a is a sister of b Symb 5.018: The product of distinct positive integers is less than their sum if and only if one of

them is equal to its square. a2: the product of a and b. b2: the sum of a and b. c1: the square of a. F1: a is a positive integer. G2: a is less than b Symb 5.020: There is exactly one even prime number. F1: a is even. G1: a is prime. H1: a is a number. Symb 5.021: There is exactly one even number, and it is prime. F1: a is even. G1: a is prime. H1: a is a number Symb 5.022: No monogamous person has more than one spouse. F1: a is a monogamous person. G2: a is a spouse of b Symb 5.023: An opera is enjoyable if and only if it has exactly two acts. F1: a is an opera. G1: a is enjoyable. H2: a is an act of b Symb 5.024: At most one student missed at most one problem. F1: a is an student. G2: a missed b. H1: a is a problem Symb 5.025: At least two soldiers shot at least one demonstrator. F1: a is a soldier. G2: a shot b. H1: a is a demonstrator Symb 5.026: For every class x, if every member of x has a member and no two members of x

have any member in common, then there is a class y such that every member of x has exactly one member in common with y. F1: a is a class.G2: a is a member of b

Symb 5.027: Some course is taught by exactly one instructor, and some instructor teaches

exactly one course. F1: a is an instructor. G1: a is a course. H2: a teaches b Symb 5.029: There is exactly one instructor and exactly one course, and that instructor teaches

that course.


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F1: a is an instructor. G1: a is a course. H2: a teaches b Symb 5.030: There is exactly one instructor who teaches exactly one course. F1: a is an instructor. G1: a is a course. H2: a teaches b Symb 5.031: Alfred has exactly one half-brother a: Alfred. F2: a is a son of b Symb 5.032: Classes are identical if and only if they have the same members. F1: a is a class. G2: a is a member of b Symb 5.040: Emily envies those that Emily envies e: Emily. V2: a envies b Symb 5.041: Emily envies those that only Emily envies e: Emily. V2: a envies b Symb 5.042: Emily envies only those that Emily envies e: Emily. V2: a envies b Symb 5.043: Only Emily envies those that Emily envies e: Emily. V2: a envies b Symb 5.044: Emily envies only those that only Emily envies e: Emily. V2: a envies b Symb 5.045: Only Emily envies only those that Emily envies e: Emily. V2: a envies b Symb 5.046: Only Emily envies those that only Emily envies e: Emily. V2: a envies b

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Symbolization Exercises From L2K