Engineering Questions with Answers - Multiple Choice Questions

# MCQs on Logics – Implication and Double Implications

1 - Question

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

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

2 - Question

. 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

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

3 - Question

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

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

4 - Question

The statement which is logically equivalent to A∧ (and) B is?
a) A->B
b) ~A ∧ ~ B
c) A ∧ ~B
d) ~(A->~B)

Explanation: The truth table of both statements are same.

5 - Question

. 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

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

6 - Question

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)

Explanation: Hypothesis is false, hence statement is true.

7 - Question

“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

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

8 - Question

. 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

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

9 - Question

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

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

10 - Question

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)