Home › Quizzes › Propositional Logic

Propositional Logic

This quiz is designed to assess your understanding of Propositional Logic, a fundamental area of mathematical logic that deals with the study of propositions and their relationships.

15 Questions Published
Play Quiz Practise this topic out loud

Questions

Question 1 Multiple Choice (Single Answer)

In propositional logic, a proposition is a statement that is either true or false, but not both.

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

The symbol "¬" is used to denote which logical operator?

  1. Conjunction
  2. Disjunction
  3. Negation
  4. Implication
Question 3 Multiple Choice (Single Answer)

The truth table for the logical operator "∧" (conjunction) is as follows:


  1. P Q P ∧ Q
    True True True
    True False False
    False True False
    False False False

  2. P Q P ∧ Q
    True True False
    True False True
    False True True
    False False True

  3. P Q P ∧ Q
    True True True
    True False True
    False True False
    False False True

  4. P Q P ∧ Q
    True True False
    True False False
    False True True
    False False False
Question 4 Multiple Choice (Single Answer)

The logical operator "∨" (disjunction) is also known as the:

  1. Inclusive OR
  2. Exclusive OR
  3. Negation
  4. Implication
Question 5 Multiple Choice (Single Answer)

The truth table for the logical operator "→" (implication) is as follows:


  1. P Q P → Q
    True True True
    True False False
    False True True
    False False True

  2. P Q P → Q
    True True False
    True False True
    False True False
    False False True

  3. P Q P → Q
    True True True
    True False True
    False True True
    False False False

  4. P Q P → Q
    True True False
    True False False
    False True True
    False False False
Question 6 Multiple Choice (Single Answer)

The logical operator "↔" (biconditional) is equivalent to which of the following compound propositions?

  1. (P ∧ Q) ∨ (¬P ∧ ¬Q)
  2. (P → Q) ∧ (Q → P)
  3. (P ∨ Q) ∧ (¬P ∨ ¬Q)
  4. (P ∧ ¬Q) ∨ (¬P ∧ Q)
Question 7 Multiple Choice (Single Answer)

In propositional logic, a tautology is a compound proposition that is always true, regardless of the truth values of its component propositions.

  1. True
  2. False
Question 8 Multiple Choice (Single Answer)

The following proposition is an example of a tautology:

  1. (P ∨ ¬P)
  2. (P ∧ Q) → P
  3. (P → Q) → ¬Q
  4. (P ∨ Q) ∧ (¬P ∨ ¬Q)
Question 9 Multiple Choice (Single Answer)

A contradiction is a compound proposition that is always false, regardless of the truth values of its component propositions.

  1. True
  2. False
Question 10 Multiple Choice (Single Answer)

The following proposition is an example of a contradiction:

  1. (P ∧ ¬P)
  2. (P → Q) → ¬Q
  3. (P ∨ Q) ∧ (¬P ∨ ¬Q)
  4. (P ∧ Q) → P
Question 11 Multiple Choice (Single Answer)

In propositional logic, a contingency is a compound proposition that is neither a tautology nor a contradiction.

  1. True
  2. False
Question 12 Multiple Choice (Single Answer)

The following proposition is an example of a contingency:

  1. (P ∨ ¬P)
  2. (P ∧ Q) → P
  3. (P → Q) → ¬Q
  4. (P ∨ Q) ∧ (¬P ∨ ¬Q)
Question 13 Multiple Choice (Single Answer)

The distributive law in propositional logic states that:

  1. (P ∨ (Q ∧ R)) = (P ∨ Q) ∧ (P ∨ R)
  2. (P ∧ (Q ∨ R)) = (P ∧ Q) ∨ (P ∧ R)
  3. (P → (Q ∧ R)) = (P → Q) ∧ (P → R)
  4. (P ∨ (Q → R)) = (P ∨ Q) → (P ∨ R)
Question 14 Multiple Choice (Single Answer)

The associative law in propositional logic states that:

  1. (P ∨ (Q ∨ R)) = (P ∨ Q) ∨ R
  2. (P ∧ (Q ∧ R)) = (P ∧ Q) ∧ R
  3. (P → (Q → R)) = (P → Q) → R
  4. (P ∨ (Q → R)) = (P ∨ Q) → R
Question 15 Multiple Choice (Single Answer)

The De Morgan's laws in propositional logic state that:

  1. ¬(P ∨ Q) = ¬P ∨ ¬Q and ¬(P ∧ Q) = ¬P ∧ ¬Q
  2. ¬(P → Q) = P ∨ ¬Q and ¬(P ∧ Q) = P ∨ ¬Q
  3. ¬(P → Q) = ¬P ∧ Q and ¬(P ∧ Q) = ¬P ∨ Q
  4. ¬(P → Q) = P ∧ ¬Q and ¬(P ∧ Q) = ¬P ∨ ¬Q
← Back to Quizzes