QUESTIONS OF MATHEMATIC LOGIC

1.  If the statement is false and the statement p-value qtrue, then the following statement which is false is ...A. p ∨ q  D. ~ P ∧ qB. p ⇒ q  E. ~ P ∨ ~ qC ~ p ⇒ ~ q

2.  Two statements p and q:P: is trueQ: is falseCompound statements below are true except:A. p ∨ q  D. ~ P ∧ qB. p ∧ ~ q   E. ~ (P ⇔ q)C ~ p ⇒ q

4. Negation of the statement "All people eatrice "is: ..A. "Some people do not eat rice"B. "All people do not eat rice"C. "Not all people do not eat rice"D. "Not all people eat rice"E. "Some people eat rice“

5.  Negation of: "All the students did not make the taskMathematics "is ......A. All students do not make the task matematicsB. There are students who do not make the task matematicsC. Some students make the task matematicsD. Some students do not make the task matematicsE. No student makes the task matematics

5. The inverse of "if it rains then the road in front of the school muddy "is ...A. If the road in front of the rain did not tarnish the school downB. It did not rain and muddy road in front of the schoolC. If it did not rain the road in front of the school tarnishD. If it did not rain the road in front of the school does not tarnishE. It did not rain or road in front of the school is not tarnish

6. Statement equivalent to "If Amir diligenthe's smart to learn it "is ...A. If Amir lazy to learn then he is stupidB. If Amir studious he is not smartC. If Amir does not study hard so he's smartD. If Amir was not good so he did not study hardE. If Amir was not good so he studied diligently.

7. The convers of the phrase "If he was a Dutchman and he Europeans "are .....A. If he is not European so he was not NetherlandsB. If he is not then he is certainly the Netherlands EuropeC. If it is not Dutch so he was not EuropeD. If he is Dutch and he is not necessarily the NetherlandsE. If he is a European so he is dutchman

8. Contraposition of (~ p ⇒ q) ⇒ (p ∨ ~ q) is ....A. (p ∧ q) ⇒ (p ⇒ ~ q)B. (p ⇒ ~ q) ⇒ (p ⇒ ~ q)C. (p ⇒ ~ q) ⇒ (p ⇒ q)D. (~ p ⇒ ~ q) ⇒ (p ∧ ~ q)E. (p ∧ ~ q) ⇒ (~ p ∧ ~ q)

8. Contraposition of (~ p ⇒ q) ⇒ (p ∨ ~ q) is ....A. (p ∧ q) ⇒ (p ⇒ ~ q)B. (p ⇒ ~ q) ⇒ (p ⇒ ~ q)C. (p ⇒ ~ q) ⇒ (p ⇒ q)D. (~ p ⇒ ~ q) ⇒ (p ∧ ~ q)E. (p ∧ ~ q) ⇒ (~ p ∧ ~ q)

9. Conclusion of three premises:(1) p ⇒ q (2) q ⇒ r (3) ~ rA. p  B. q C. r  D. ~ p E. ~ r

10. Inferences from the premises is…..

A. p  C. q E. ~ (p ∨ q)

B. ~ p  D. ~ q

11. (~ pvq)^(pv ~ q) is equivalent to the statement ..a. p  ⇒ q b. p  ⇒ ~ q c. ~ p  ⇒ q

d. ~ p ⇒ ~ q e. p  ⇔ q

 12. q v ~ p statements are equivalent to the

statement ..a. ~p ⇒~q b. q ∧ ~p c. ~q ⇒ ~pd. q ⇒ ~p e. ~q v ~p

13. In the table below, the truth value for the column~p  ∧ ~ q from left to right are ..

a. F T F F b. F F T T c. F F F Td. F T F T e. F T T T

14. The truth value of p ∧ ~ q are equivalent to the statement ..

a. p ⇒ q b. ~ p ⇒ ~ q c. q ⇒ ~ p

d. p ⇒ ~ q e. ~ ( p ⇒ q)

p Q~p ˄~ q

T TT FF TF F

15. The truth of (p ⇒ q) V ~q is equivalent with ..

A. TautologyB. ContradictionC. ~pD. ~qE. (p V q)

THE ANSWERS ...

1. To be able to answer the questions of logic, this table mustunderstand (not memorize):

Create a table for the above problem by basing the required tableunderstood the above:

which is false is ~ p ⇒ ~ q?  C

2. Everything is true but there is a wrong one, we find that wrong.Create a table:

Note:(P ⇔ q statement that is false is notanswer as to facilitate the statement~ (P ⇔ q) )Seen from the table that is false isstatement~ P ∧ q?  D

3. Remember!Quantifier sentence negation:~ (all p) ⇒ no / some ~ p~ (no / some p) ⇒ all ~ p- All negation is no / few- Eat rice ⇒ p = ~ p = not eat riceso its negation: no / some people do not eat rice.The answer is A

4. - All existing negation / a- Do not make the task of curricular negation makes the taskmatematicsSo the negation of the sentence above:None / some students make the task cocuriculerThe answer is C

5.Theory:Konvers: p ⇒ qInverse: ~ p ⇒ ~ qContraposition: ~ p ~ q ⇒Equivalence: p ⇒ q = ~ q ~ p ⇒on the inverse problem means:p = if rain falls, ~ p = if it did not rainq = muddy road in front of the school, ~ q = road aheadschool does not tarnishthe answer is ~ p ⇒ ~ q:if it did not rain the road in front of the school is nottarnishThe answer is D

6. According to the theoryEquivalence: p ⇒ q = ~ q ⇒ ~ pp = if Amir studious, ~ p = Amir did not study hardq = smart, ~ q = not smartthe answer is: ~ q ⇒ ~ pif Amir doesn’t smart then Amir is not diligentthe answer is D

7. Convers: p ⇒ qp = the Netherlands, q = a European(Not required ingkaran sentence)then the answer is q ⇒ p :If he is a European Dutchman then heThe answer is E

8. Contraposition is ~ q ⇒ ~ p:Suppose p = (~ p ⇒ q) then ~ p = ~ (~ p ⇒ q)= ~ P ∧ ~ qThis theory must be understood: negation:

or:~ (p ∨ q) = ~ p ∧ ~ q ..... (5)~ (p ∧ q) = ~ p ∨ ~ q ..... (6)~ (p ⇒ q) = p ∧ ~ q ..... (7)Suppose p = (~ p ⇒ q), ~ p = ~ (~ p ⇒ q)= ~ P ∧ ~ q(see .. (1) conditions remain p, q be the opposite)and turned into ∧q = (~ p ∨ q), ~ q = ~ (~ p ∨ q)= P ∧ ~ q(see ... (5) p and q changes the sign of all, the operationturned into ∧The answer is ~ p ~ q ⇒namely:⇒ p ∧ ~ q ~ p ∧ ~ qThe answer is E.

9.p ⇒ qq ⇒ r~ r∴?Step 1:p ⇒ qq ⇒ r∴ p ⇒ r ? Sillogismestep 2:p ⇒ r~ r∴ ~ p? tollensthe answer is D

10. Equivalent: ~ p ∨ p ⇒ q ≡ qThen p ∨ q ≡ ~ p ⇒ q ≡ ~ q ⇒ pStatement negationp ∧ q ⇒ p ~ q ..... (1)q ⇒ p ∧ q ~ p .... (2)~ p ⇒ ~ q ~ p ∧ ~ q ..... (3)~ ~ p ~ q ⇒ p ∧ q ..... (4)

becames:

the answer is p (A)

11. (~p v q) ^ (p v ~q) = T

FFT

E. p ⇔ q = TFFT

The Answer Is E

12. q v ~ p = FTTT

Equivalent withd. q ⇒ ~p = F

TTT

13.

So the answer is C

P Q~p ˄~ q

T T F

T F F

F T F

F F T

14. p ∧ ~ q = F TFF

EQUIVALENT WITH

B. ~p ⇒~q = FTFF

So the answer is B

15.

(p > q) v ~q

T T T T F

T F F T T

F T T T F

F T F T T

THE ANSWER IS A (TAUTOLOGY)