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Alejandro Gonzalez M2 Algebra
Geo Journal 2
Conditional if then statements
A conditional statement or if then statements is a statement written in the for of if P then Q. In a statement P is the hypothesis and Q is the conclusion.
Ex 1: If you clean the dog then you may go to the park.
Ex 2: If you do your homework you may go with your friends to the movies.
Ex 3: If you eat the spinach then you may have a candy.
Counterexamples
A counterexample is a example that says and proves that the conjecture is wrong.
Ex 1: If you don't watch the movie then you won't know about it. False because they might say to you what's the movie about.
Ex 2: If you don't have a bath you will smell bad. False because you can use deodorant.
Ex 3: If you don't put away your school materials then you will be late tomorrow morning. False because you can e
What is a definition?
A definition has the description or meaning of something.
Ex 1: Carbon dioxide is the compound that animals exhale after inhaling oxygen.
Ex 2: Wood is a material extracted from trees.
Ex 3: Coffe is drink that comes has caffeine.
Biconditional statements
A Biconditional statement is a statement that can't be contradicted and it's written P if and only if Q. They are used to show that the hypothesis depends on the conclusion to determine if the statement is valid or invalid. They are important because they are very specific so your answer will always be the same.
Ex 1: You get good grades if and only if you go to school every day.
Ex 2: You have friends if and only if you talk with people.
Ex 3: You are healthy if and only if you do exercise.
Deductive reasoning
Deductive reasoning is when you use observations to make a conclusion. Inductive reasoning is when you use facts to make conclusions.
Ex 1: They say that Lamborghini was founded after Ferrari because of competition to see whitch car was better. This is inductive reasoning because it is a fact.
Ex 2: All of the music has instruments therefore all of the instruments make music. This is deductive reasoning because it's based on observations.
Ex 3: Water creates moisture therefore all of the moisture is from water. This is deductive reasoning because it is based on observations.
laws of logic
The law of Detachment is if p then q is a true statement and p is true then q is true.
Ex 1: If you eat less you lose weight. Rona lost weight because she ate less.
Ex 2: If you have internet then you have a computer. Bob has a computer with Internet.
Ex 3: If you take a bath then you smell good. You smell good.
Law of Syllogism says that if p then q then r are true statements then p then r are true statement.
Ex 1: You are hot then younuse A/C to cool down. You are cold because of the A/C. You are cold with an A/C
Ex 2: If you have a Veyron then you are a millionaire. You have a Veyron so younger a millionaire.
Ex 3: If an animal has hair then it's a mammal. You have hair so you are a mammal.
Algebraic proofs using the algebraic
properties of equalityProofs are a way to solve problems giving evidence of each steps to solve.
Ex 1: Subtraction property of equality, if a=b then a-c is b-c
Ex 2: Multiplication property of equality, if a=b then AC=bc
Ex 3: Reflexive property of equality, a=a
Two column proofs
In a two column proof you write the steps on the left side and the reason of the steps on the right.
Linear pair postulate (LPP)
The lPP says that two lines that form a linear pair are supplementary
Congruent complements
theoremThe theorem says that If two angles are complementary to the same angle then the 2 angles are congruent.
Congruent supplements theorem
If two angles are supplementary to the same angle then the two angles are congruent.
Vertical angles theorem
Vertical angles are congruent, the angles the non adjacent angles will have the same measurements
Common segments theorem
if segment ab is congruent to segment cd then segment ac is congruent to segment bd
Ex 1: If Chicago to Detroit is the same as Seattle to Los Angeles then Chicago to Seattle is the same as Detroit to Los Angeleles.
Ex 2: If Miami is the same distance to Orlando and Tallahassee to Tampa then Miami to Tallahassee is the same as Orlando to Tampa.
Ex 3:
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