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Boolean Algebra

This quiz covers the fundamental concepts and operations of Boolean algebra, a branch of mathematics that deals with logical operations and binary variables.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the dual of the expression (A ∨ B) ∧ (C ∧ D)?

  1. ¬(¬A ∧ ¬B) ∨ ¬(¬C ∨ ¬D)
  2. ¬(¬A ∨ ¬B) ∧ ¬(¬C ∧ ¬D)
  3. ¬(A ∧ B) ∨ ¬(C ∨ D)
  4. ¬(A ∨ B) ∧ ¬(C ∧ D)
Question 2 Multiple Choice (Single Answer)

Simplify the following Boolean expression: (A ∨ B) ∧ (¬A ∨ C)

  1. A ∨ C
  2. B ∨ C
  3. A ∨ B ∨ C
  4. ¬A ∨ B ∨ C
Question 3 Multiple Choice (Single Answer)

Construct the truth table for the following Boolean expression: (A ∧ B) ∨ (¬A ∧ C)

  1. A | B | C | (A ∧ B) ∨ (¬A ∧ C)
    --- | --- | --- | ---
    0 | 0 | 0 | 0
    0 | 0 | 1 | 1
    0 | 1 | 0 | 0
    0 | 1 | 1 | 1
    1 | 0 | 0 | 0
    1 | 0 | 1 | 1
    1 | 1 | 0 | 1
    1 | 1 | 1 | 1
  2. A | B | C | (A ∧ B) ∨ (¬A ∧ C)
    --- | --- | --- | ---
    0 | 0 | 0 | 1
    0 | 0 | 1 | 0
    0 | 1 | 0 | 1
    0 | 1 | 1 | 0
    1 | 0 | 0 | 1
    1 | 0 | 1 | 0
    1 | 1 | 0 | 0
    1 | 1 | 1 | 1
  3. A | B | C | (A ∧ B) ∨ (¬A ∧ C)
    --- | --- | --- | ---
    0 | 0 | 0 | 0
    0 | 0 | 1 | 1
    0 | 1 | 0 | 1
    0 | 1 | 1 | 0
    1 | 0 | 0 | 1
    1 | 0 | 1 | 0
    1 | 1 | 0 | 1
    1 | 1 | 1 | 0
  4. A | B | C | (A ∧ B) ∨ (¬A ∧ C)
    --- | --- | --- | ---
    0 | 0 | 0 | 1
    0 | 0 | 1 | 1
    0 | 1 | 0 | 0
    0 | 1 | 1 | 1
    1 | 0 | 0 | 0
    1 | 0 | 1 | 1
    1 | 1 | 0 | 0
    1 | 1 | 1 | 0
Question 4 Multiple Choice (Single Answer)

Which of the following is a valid Boolean identity?

  1. ¬(A ∨ B) = ¬A ∨ ¬B
  2. ¬(A ∧ B) = ¬A ∧ ¬B
  3. A ∨ B = A ∧ B
  4. A ∧ B = A ∨ B
Question 5 Multiple Choice (Single Answer)

Find the minimal sum-of-products form of the following Boolean expression: (A ∨ B) ∧ (¬A ∨ C) ∧ (B ∨ ¬C)

  1. A ∨ B ∨ C
  2. A ∨ C
  3. B ∨ C
  4. A ∨ B
Question 6 Multiple Choice (Single Answer)

What is the complement of the Boolean expression (A ∧ B) ∨ (¬A ∧ C)?

  1. ¬(A ∧ B) ∧ ¬(¬A ∧ C)
  2. ¬(A ∧ B) ∨ ¬(¬A ∧ C)
  3. (A ∨ B) ∧ (¬A ∨ C)
  4. (A ∨ B) ∨ (¬A ∨ C)
Question 7 Multiple Choice (Single Answer)

Which of the following Boolean expressions is equivalent to ¬(A ⊕ B)?

  1. A ∨ B
  2. A ∧ B
  3. ¬A ∧ ¬B
  4. ¬A ∨ ¬B
Question 8 Multiple Choice (Single Answer)

Simplify the following Boolean expression using Boolean algebra: (A ∨ B) ∧ (¬A ∨ ¬B)

  1. 0
  2. 1
  3. A ∨ B
  4. ¬A ∨ ¬B
Question 9 Multiple Choice (Single Answer)

Which of the following is a valid Boolean law?

  1. Associative law of addition
  2. Associative law of multiplication
  3. Distributive law of addition over multiplication
  4. Distributive law of multiplication over addition
Question 10 Multiple Choice (Single Answer)

What is the dual of the Boolean expression (A ∧ B) ∨ (¬A ∧ C)?

  1. ¬(¬A ∨ ¬B) ∧ ¬(A ∨ ¬C)
  2. ¬(¬A ∨ ¬B) ∨ ¬(A ∨ ¬C)
  3. ¬(A ∨ B) ∧ ¬(¬A ∨ C)
  4. ¬(A ∨ B) ∨ ¬(¬A ∨ C)
Question 11 Multiple Choice (Single Answer)

Simplify the following Boolean expression: (A ∨ B) ∧ (¬A ∨ C) ∧ (B ∨ ¬C)

  1. A ∨ B ∨ C
  2. A ∨ C
  3. B ∨ C
  4. A ∨ B
Question 12 Multiple Choice (Single Answer)

Which of the following is a valid Boolean identity?

  1. ¬(A ∨ B) = ¬A ∨ ¬B
  2. ¬(A ∧ B) = ¬A ∧ ¬B
  3. A ∨ B = A ∧ B
  4. A ∧ B = A ∨ B
Question 13 Multiple Choice (Single Answer)

Find the minimal sum-of-products form of the following Boolean expression: (A ∨ B) ∧ (¬A ∨ C) ∧ (B ∨ ¬C)

  1. A ∨ B ∨ C
  2. A ∨ C
  3. B ∨ C
  4. A ∨ B
Question 14 Multiple Choice (Single Answer)

What is the complement of the Boolean expression (A ∧ B) ∨ (¬A ∧ C)?

  1. ¬(A ∧ B) ∧ ¬(¬A ∧ C)
  2. ¬(A ∧ B) ∨ ¬(¬A ∧ C)
  3. (A ∨ B) ∧ (¬A ∨ C)
  4. (A ∨ B) ∨ (¬A ∨ C)
Question 15 Multiple Choice (Single Answer)

Which of the following Boolean expressions is equivalent to ¬(A ⊕ B)?

  1. A ∨ B
  2. A ∧ B
  3. ¬A ∧ ¬B
  4. ¬A ∨ ¬B
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