# Symbolic Logic MCQs with Answers

Symbolic Logic MCQs are very important test and often asked by various testing services and competitive exams around the world. Here you will find all the Important Symbolic Logic MCQs for Preparation.

The student can clear their concepts for Symbolic Logic online quiz by attempting it. Doing MCQs based Symbolic Logic will help you to check your understanding and identify areas of improvement.

## Symbolic Logic Online MCQs with Answers

Which symbol represents the logical connective “conjunction” (AND)?
a) ∧
b) ∨
c) ¬
d) →

a) ∧

Which symbol represents the logical connective “disjunction” (OR)?
a) ∧
b) ∨
c) ¬
d) →

b) ∨

Which symbol represents the logical connective “negation” (NOT)?
a) ∧
b) ∨
c) ¬
d) →

c) ¬

Which symbol represents the logical connective “implication” (IF-THEN)?
a) ∧
b) ∨
c) ¬
d) →

d) →

What is the truth value of the statement “p ∧ q” if p is true and q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of the statement “p ∨ q” if p is true and q is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

What is the truth value of the statement “¬p” if p is true?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of the statement “p → q” if p is true and q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of the statement “¬(p ∧ q)” if p is true and q is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

What is the truth value of the statement “p ∨ (q ∧ ¬p)” if p is true and q is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

Which symbol represents the logical connective “biconditional” (IF AND ONLY IF)?
a) ∧
b) ∨
c) ¬
d) ↔

d) ↔

Which logical operator represents the “AND” operation?
a) ∧
b) ∨
c) ¬
d) ⊕

a) ∧

Which logical operator represents the “OR” operation?
a) ∧
b) ∨
c) ¬
d) ⊕

b) ∨

Which logical operator represents the “NOT” operation?
a) ∧
b) ∨
c) ¬
d) ⊕

c) ¬

Which logical operator represents the “XOR” (exclusive OR) operation?
a) ∧
b) ∨
c) ¬
d) ⊕

d) ⊕

What is the negation of the statement “P ∨ Q”?
a) ¬P ∧ ¬Q
b) ¬P ∨ ¬Q
c) ¬(P ∨ Q)
d) ¬(P ∧ Q)

c) ¬(P ∨ Q)

What is the negation of the statement “P ∧ Q”?
a) ¬P ∨ ¬Q
b) ¬P ∧ ¬Q
c) ¬(P ∨ Q)
d) ¬(P ∧ Q)

d) ¬(P ∧ Q)

Which statement is equivalent to “P → Q”?
a) P ∨ Q
b) P ∧ Q
c) ¬P ∨ Q
d) ¬P ∧ Q

c) ¬P ∨ Q

Which statement is equivalent to “P ↔ Q”?
a) P ∨ Q
b) P ∧ Q
c) P → Q
d) (P ∧ Q) ∨ (¬P ∧ ¬Q)

d) (P ∧ Q) ∨ (¬P ∧ ¬Q)

What is the truth value of “P ∧ Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “P ∨ Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

What is the truth value of “P → Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “P ↔ Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “¬P” if P is true?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “¬P” if P is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

What is the truth value of “P ∧ ¬P”?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “P ∨ ¬P”?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

Which of the following is the contrapositive of the statement “If P, then Q”?
a) If ¬P, then ¬Q
b) If ¬Q, then ¬P
c) If Q, then P
d) If P, then ¬Q

a) If ¬P, then ¬Q

Which of the following is the converse of the statement “If P, then Q”?
a) If ¬P, then ¬Q
b) If ¬Q, then ¬P
c) If Q, then P
d) If P, then ¬Q

c) If Q, then P

Which of the following is the inverse of the statement “If P, then Q”?
a) If ¬P, then ¬Q
b) If ¬Q, then ¬P
c) If Q, then P
d) If P, then ¬Q

d) If P, then ¬Q

Which of the following is the contrapositive of the statement “If P ↔ Q, then R”?
a) If ¬R, then ¬P ↔ Q
b) If ¬P ↔ Q, then R
c) If R, then P ↔ Q
d) If P ↔ Q, then ¬R

a) If ¬R, then ¬P ↔ Q

Which of the following is the converse of the statement “If P ↔ Q, then R”?
a) If ¬R, then ¬P ↔ Q
b) If ¬P ↔ Q, then R
c) If R, then P ↔ Q
d) If P ↔ Q, then ¬R

c) If R, then P ↔ Q

Which logical operator represents the “AND” operation?
a) ∧
b) ∨
c) ¬
d) ⊕

a) ∧

Which logical operator represents the “OR” operation?
a) ∧
b) ∨
c) ¬
d) ⊕

b) ∨

Which logical operator represents the “NOT” operation?
a) ∧
b) ∨
c) ¬
d) ⊕

c) ¬

Which logical operator represents the “XOR” (exclusive OR) operation?
a) ∧
b) ∨
c) ¬
d) ⊕

d) ⊕

What is the negation of the statement “P ∨ Q”?
a) ¬P ∧ ¬Q
b) ¬P ∨ ¬Q
c) ¬(P ∨ Q)
d) ¬(P ∧ Q)

c) ¬(P ∨ Q)

What is the negation of the statement “P ∧ Q”?
a) ¬P ∨ ¬Q
b) ¬P ∧ ¬Q
c) ¬(P ∨ Q)
d) ¬(P ∧ Q)

d) ¬(P ∧ Q)

Which statement is equivalent to “P → Q”?
a) P ∨ Q
b) P ∧ Q
c) ¬P ∨ Q
d) ¬P ∧ Q

c) ¬P ∨ Q

Which statement is equivalent to “P ↔ Q”?
a) P ∨ Q
b) P ∧ Q
c) P → Q
d) (P ∧ Q) ∨ (¬P ∧ ¬Q)

d) (P ∧ Q) ∨ (¬P ∧ ¬Q)

What is the truth value of “P ∧ Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “P ∨ Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

What is the truth value of “P → Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “P ↔ Q” if P is true and Q is false?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “¬P” if P is true?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “¬P” if P is false?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

What is the truth value of “P ∧ ¬P”?
a) True
b) False
c) Uncertain
d) Not applicable

b) False

What is the truth value of “P ∨ ¬P”?
a) True
b) False
c) Uncertain
d) Not applicable

a) True

Which of the following is the contrapositive of the statement “If P, then Q”?
a) If ¬P, then ¬Q
b) If ¬Q, then ¬P
c) If Q, then P
d) If P, then ¬Q

a) If ¬P, then ¬Q

Which of the following is the converse of the statement “If P, then Q”?
a) If ¬P, then ¬Q
b) If ¬Q, then ¬P
c) If Q, then P
d) If P, then ¬Q

c) If Q, then P

Which of the following is the inverse of the statement “If P, then Q”?
a) If ¬P, then ¬Q
b) If ¬Q, then ¬P
c) If Q, then P
d) If P, then ¬Q

d) If P, then ¬Q

Which of the following is the contrapositive of the statement “If P ↔ Q, then R”?
a) If ¬R, then ¬P ↔ Q
b) If ¬P ↔ Q, then R
c) If R, then P ↔ Q
d) If P ↔ Q, then ¬R

a) If ¬R, then ¬P ↔ Q

Which of the following is the converse of the statement “If P ↔ Q, then R”?
a) If ¬R, then ¬P ↔ Q
b) If ¬P ↔ Q, then R
c) If R, then P ↔ Q
d) If P ↔ Q, then ¬R