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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
  3. Contradiction
  4. Binomial

Answer: B) Tautology

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

Answer: C) Final

Explanation:

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


3. _____ are statements that are always false?

  1. Boolean
  2. Negation
  3. Contradiction
  4. Tautology

Answer: C) Contradiction

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.




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