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Discrete mcqs 2

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“Implication and Double Implications”.
1. 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
View Answer
Answer: c
Explanation: Both of them have same truth table, Hence they are equal.
2. 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
View Answer
Answer: a
Explanation: A->P is logically equivalent to ~A v P.
3. 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
View Answer
Answer: c
Explanation: For implications to be false hypothesis should be true and conclusion should be false.
4. The statement which is logically equivalent to A (and) B is
a) A->B
b) ~A ~ B
c) A ~B
d) ~(A->~B)
View Answer

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Answer: d
Explanation: The truth table of both statements are same.
5. 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
View Answer
Answer: c
Explanation: If and only if statements are bi-conditionals.
6. Let P, Q, R be true, false true , respectively, which of the following is true
a) PQR
b) P~Q~R
c) Q->(PR)
d) P->(QR)
View Answer
Answer: c
Explanation: Hypothesis is false, hence statement is true.
7. “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.
View Answer
Answer: a
Explanation: Negation of P->Q is P~Q.
8. Consider the following statements
A: Raju should exercise.
B: Raju is not a decent table tennis player.

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“Implication and Double Implications”. 1. Let P and Q be statements, then PQ is logically equivalent to a) P~Q b) ~PQ c) ~P~Q d) None of the mentioned View Answer Answer: c Explanation: Both of them have same truth table, Hence they are equal. 2. 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 View Answer Answer: a Explanation: A->P is logically equivalent to ~A v P. 3. 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 View Answer Answer: c Explanation: For implications to be false hypothesis should be true and conclusion should be false. 4. The statement which is logically equivalent to A∧ (and) B is a) A->B b) ~A ∧ ~ B c) A ∧ ~B d) ~(A->~B) View Answer Answer: d Explanation: The truth table of both statements are same. 5. 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) QP d) ~P v Q View Answer Answer: c Explanation: If and only if statements are bi-conditionals. 6. 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) View Answer Answer: c Explanation: Hypothesis is false, hence statement is true. 7. “Match will be played only if it is not a humid day.” Th ...
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