# Discrete Mathematics | Tautologies and Contradiction MCQs

Discrete Mathematics | Tautologies and Contradiction MCQs: This section contains multiple-choice questions and answers on Tautologies and Contradiction in Discrete Mathematics.
Submitted by Anushree Goswami, on July 18, 2022

1. If proposition P is true under all circumstances, it is a ____?

1. Boolean
2. Tautology
4. Binomial

Explanation:

If proposition P is true under all circumstances, it is a tautology.

2. The truth table contains only T in the ____ column in tautology?

1. Initial
2. Middle
3. Final
4. None

Explanation:

The truth table contains only T in the final column in tautology.

3. _____ are statements that are always false?

1. Boolean
2. Negation
4. Tautology

Explanation:

Contradictions are statements that are always false.

4. Contingencies are statements that are ____ based on the truth values of their variables?

1. True
2. False
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Contingencies are statements that are true or false based on the truth values of their variables.

5. If p is ___ and q is ____, then (p→q)⟷( ~q⟶~p) is true?

1. True, false
2. False, true
3. True, true
4. All of the above

Answer: D) All of the above

Explanation:

1. If p is true and q is false, then (p→q)⟷( ~q⟶~p) is true.
2. If p is false and q is true, then (p→q)⟷( ~q⟶~p) is true.
3. If p is true and q is true, then (p→q)⟷( ~q⟶~p) is true.

6. If p is ___ and ~p is ____, then p ∧∼p is false?

1. True, false
2. False, true
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

If p is true and ~p is false, then p ∧∼p is false and if p is false and ~p is true, then also p ∧∼p is false.

7. If p is ___ and q is ____, then (p→q)⟶ (p∧q) is true?

1. True, true
2. True, false
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

1. If p is true and q is true, then (p→q)⟶ (p∧q) is true.
2. If p is false and q is false, then (p→q)⟶ (p∧q) is true.

8. If p is ___ and q is ____, then (p→q)⟶ (p∧q) is false?

1. False, false
2. False, true
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

1. If p is false and q is false, then (p→q)⟶ (p∧q) is false.
2. If p is false and q is true, then (p→q)⟶ (p∧q) is false.