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Propositional Logic: Truth Tables and Logical Equivalence

This quiz will test your understanding of propositional logic, truth tables, and logical equivalence.

13 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the truth value of the following proposition: ∼(P ∨ Q) ∧ ∉P?

  1. True
  2. False
  3. Indeterminate
Question 2 Multiple Choice (Single Answer)

Construct a truth table for the following proposition: (P ∨ Q) ∧ ∉P.

  1. | P | Q | (P ∨ Q) | ∉P | (P ∨ Q) ∧ ∉P |
    |---|---|---|---|---|
    | T | T | T | F | F |
    | T | F | F | F | T |
    | F | T | F | T | F |
    | F | F | F | T | T |
  2. | P | Q | (P ∨ Q) | ∉P | (P ∨ Q) ∧ ∉P |
    |---|---|---|---|---|
    | T | T | T | F | F |
    | T | F | F | F | T |
    | F | T | T | T | F |
    | F | F | F | T | T |
  3. | P | Q | (P ∨ Q) | ∉P | (P ∨ Q) ∧ ∉P |
    |---|---|---|---|---|
    | T | T | T | F | T |
    | T | F | F | F | T |
    | F | T | T | T | F |
    | F | F | F | T | T |
Question 3 Multiple Choice (Single Answer)

Which of the following is logically equivalent to the proposition ∼(P ∨ Q)?

  1. P ∨ Q
  2. P ∧ Q
  3. ∉(P ∨ Q)
  4. ∉P ∧ ∉Q
Question 4 Multiple Choice (Single Answer)

Construct a truth table for the following proposition: (P ∧ Q) ∨ (∉P ∧ ∉Q).

  1. | P | Q | (P ∧ Q) | (∉P ∧ ∉Q) | (P ∧ Q) ∨ (∉P ∧ ∉Q) |
    |---|---|---|---|---|
    | T | T | T | F | F |
    | T | F | F | T | F |
    | F | T | F | T | F |
    | F | F | T | T | T |
  2. | P | Q | (P ∧ Q) | (∉P ∧ ∉Q) | (P ∧ Q) ∨ (∉P ∧ ∉Q) |
    |---|---|---|---|---|
    | T | T | T | F | T |
    | T | F | F | T | F |
    | F | T | F | T | F |
    | F | F | T | T | T |
  3. | P | Q | (P ∧ Q) | (∉P ∧ ∉Q) | (P ∧ Q) ∨ (∉P ∧ ∉Q) |
    |---|---|---|---|---|
    | T | T | T | F | T |
    | T | F | F | T | T |
    | F | T | F | T | T |
    | F | F | T | T | T |
Question 5 Multiple Choice (Single Answer)

Which of the following is logically equivalent to the proposition (P ∨ Q) ∧ (∉P ∧ ∉Q)?

  1. P ∧ Q
  2. P ∨ Q
  3. ∼(P ∧ Q)
  4. ∼(P ∨ Q)
Question 6 Multiple Choice (Single Answer)

Construct a truth table for the following proposition: (∉P ∨ ∉Q) ∧ (P ∨ Q).

  1. | P | Q | (∉P ∨ ∉Q) | (P ∨ Q) | (∉P ∨ ∉Q) ∧ (P ∨ Q) |
    |---|---|---|---|---|
    | T | T | F | T | F |
    | T | F | T | F | F |
    | F | T | T | F | F |
    | F | F | T | F | T |
  2. | P | Q | (∉P ∨ ∉Q) | (P ∨ Q) | (∉P ∨ ∉Q) ∧ (P ∨ Q) |
    |---|---|---|---|---|
    | T | T | F | T | T |
    | T | F | T | F | F |
    | F | T | T | F | F |
    | F | F | T | F | T |
  3. | P | Q | (∉P ∨ ∉Q) | (P ∨ Q) | (∉P ∨ ∉Q) ∧ (P ∨ Q) |
    |---|---|---|---|---|
    | T | T | F | T | F |
    | T | F | T | F | T |
    | F | T | T | F | T |
    | F | F | T | F | T |
Question 7 Multiple Choice (Single Answer)

Which of the following is logically equivalent to the proposition (∉P ∨ ∉Q) ∧ (P ∨ Q)?

  1. P ∧ Q
  2. P ∨ Q
  3. ∼(P ∧ Q)
  4. ∼(P ∨ Q)
Question 8 Multiple Choice (Single Answer)

Construct a truth table for the following proposition: (P ∧ Q) ∨ (P ∨ ∉Q).

  1. | P | Q | (P ∧ Q) | (P ∨ ∉Q) | (P ∧ Q) ∨ (P ∨ ∉Q) |
    |---|---|---|---|---|
    | T | T | T | T | T |
    | T | F | F | T | F |
    | F | T | F | T | F |
    | F | F | T | T | T |
  2. | P | Q | (P ∧ Q) | (P ∨ ∉Q) | (P ∧ Q) ∨ (P ∨ ∉Q) |
    |---|---|---|---|---|
    | T | T | T | T | T |
    | T | F | F | F | F |
    | F | T | F | T | F |
    | F | F | T | T | T |
  3. | P | Q | (P ∧ Q) | (P ∨ ∉Q) | (P ∧ Q) ∨ (P ∨ ∉Q) |
    |---|---|---|---|---|
    | T | T | T | T | T |
    | T | F | F | F | T |
    | F | T | F | T | T |
    | F | F | T | T | T |
Question 9 Multiple Choice (Single Answer)

Which of the following is logically equivalent to the proposition (P ∧ Q) ∨ (P ∨ ∉Q)?

  1. P ∧ Q
  2. P ∨ Q
  3. ∼(P ∧ Q)
  4. ∼(P ∨ Q)
Question 10 Multiple Choice (Single Answer)

Construct a truth table for the following proposition: (∉P ∨ ∉Q) ∨ (P ∧ ∉Q).

  1. | P | Q | (∉P ∨ ∉Q) | (P ∧ ∉Q) | (∉P ∨ ∉Q) ∨ (P ∧ ∉Q) |
    |---|---|---|---|---|
    | T | T | F | F | F |
    | T | F | T | T | T |
    | F | T | T | T | T |
    | F | F | T | T | T |
  2. | P | Q | (∉P ∨ ∉Q) | (P ∧ ∉Q) | (∉P ∨ ∉Q) ∨ (P ∧ ∉Q) |
    |---|---|---|---|---|
    | T | T | F | F | T |
    | T | F | T | T | T |
    | F | T | T | T | T |
    | F | F | T | T | T |
  3. | P | Q | (∉P ∨ ∉Q) | (P ∧ ∉Q) | (∉P ∨ ∉Q) ∨ (P ∧ ∉Q) |
    |---|---|---|---|---|
    | T | T | F | F | F |
    | T | F | T | T | F |
    | F | T | T | T | F |
    | F | F | T | T | T |
Question 11 Multiple Choice (Single Answer)

Which of the following is logically equivalent to the proposition (∉P ∨ ∉Q) ∨ (P ∧ ∉Q)?

  1. P ∧ Q
  2. P ∨ Q
  3. ∼(P ∧ Q)
  4. ∼(P ∨ Q)
Question 12 Multiple Choice (Single Answer)

Construct a truth table for the following proposition: (P ∨ Q) ∧ (∉P ∨ Q).

  1. | P | Q | (P ∨ Q) | (∉P ∨ Q) | (P ∨ Q) ∧ (∉P ∨ Q) |
    |---|---|---|---|---|
    | T | T | T | F | F |
    | T | F | F | T | F |
    | F | T | F | T | F |
    | F | F | F | F | T |
  2. | P | Q | (P ∨ Q) | (∉P ∨ Q) | (P ∨ Q) ∧ (∉P ∨ Q) |
    |---|---|---|---|---|
    | T | T | T | F | T |
    | T | F | F | T | F |
    | F | T | F | T | F |
    | F | F | F | F | T |
  3. | P | Q | (P ∨ Q) | (∉P ∨ Q) | (P ∨ Q) ∧ (∉P ∨ Q) |
    |---|---|---|---|---|
    | T | T | T | F | F |
    | T | F | F | T | T |
    | F | T | F | T | T |
    | F | F | F | F | T |
Question 13 Multiple Choice (Single Answer)

Which of the following is logically equivalent to the proposition (P ∨ Q) ∧ (∉P ∨ Q)?

  1. P ∧ Q
  2. P ∨ Q
  3. ∼(P ∧ Q)
  4. ∼(P ∨ Q)
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