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# MCQs on Logics – Implication and Double Implications

Let P and Q be statements, then P<->Q is logically equivalent to __________

a) P<->~Q

b) ~P<->Q

c) ~P<->~Q

d) None of the mentioned

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Answer: c

Explanation: Both of them have same truth table, Hence they are equal.

. What is the negation of the statement A->(B v(or) C)?

a) A ∧ ~B ∧ ~C

b) A->B->C

c) ~A ∧ B v C

d) None of the mentioned

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Answer: a

Explanation: A->P is logically equivalent to ~A v P.

The compound statement A-> (A->B) is false, then the truth values of A, B are respectively _________

a) T, T

b) F, T

c) T, F

d) F, F

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Answer: c

Explanation: For implications to be false hypothesis should be true and conclusion should be false.

The statement which is logically equivalent to A∧ (and) B is?

a) A->B

b) ~A ∧ ~ B

c) A ∧ ~B

d) ~(A->~B)

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Answer: d

Explanation: The truth table of both statements are same.

. Let P: We give a nice overall squad performance, Q: We will win the match.

Then the symbolic form of “We will win the match if and only if we give a nice overall squad performance.“ is?

a) P v Q

b) Q ∧ P

c) Q<->P

d) ~P v Q

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Answer: c

Explanation: If and only if statements are bi-conditionals.

Let P, Q, R be true, false true, respectively, which of the following is true?

a) P∧Q∧R

b) P∧~Q∧~R

c) Q->(P∧R)

d) P->(Q∧R)

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Answer: c

Explanation: Hypothesis is false, hence statement is true.

“Match will be played only if it is not a humid day.” The negation of this statement is?

a) Match will be played but it is a humid day

b) Match will be played or it is a humid day

c) All of the mentioned statement are correct

d) None of the mentioned

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Answer: a

Explanation: Negation of P->Q is P∧~Q.

. Consider the following statements.

A: Raju should exercise.

B: Raju is not a decent table tennis player.

C: Raju wants to play good table tennis.

The symbolic form of “Raju is not a decent table tennis player and if he wants to play good table tennis then he should exercise.” is?

a) A->B->C

b) B∧(C->A)

c) C->B∧A

d) B<->A∧C

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Answer: b

Explanation: For conditionals statement (if then), implications are used.

The statement (~P<->Q)∧~Q is true when?

a) P: True Q: False

b) P: True Q: True

c) P: False Q: True

d) P: False Q: False

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Answer: a

Explanation: For a bi-conditional to be true both inputs should be same.

Let P, Q, R be true, false, false, respectively, which of the following is true?

a) P∧(Q∧~R)

b) (P->Q)∧~R

c) Q<->(P∧R)

d) P<->(QvR)

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Answer: c

Explanation: For a bi-conditional to be true both inputs should be the same.