De Morgan’s and Distributive Simplification Quiz

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 15 | Updated: Dec 1, 2025
Please wait...
Question 1 / 15
0 %
0/100
Score 0/100
1) Simplify ¬(A ∧ B)

Explanation

According to De Morgan's law, the negation of a conjunction is the disjunction of the negations. Therefore, ¬(A ∧ B) is equivalent to ¬A ∨ ¬B.

Submit
Please wait...
About This Quiz
Simplification Rules Quizzes & Trivia

Think you can recognize deeper patterns inside brackets and negations? This quiz gives you plenty of practice applying De Morgan’s laws, distributive laws, and factoring tricks to simplify more involved Boolean expressions. You’ll rewrite negations like ¬(A ∧ B) and ¬(A ∨ B), distribute terms across ∧ and ∨, and... see morefactor common parts out of expressions such as (A ∧ B) ∨ (A ∧ C) or (A ∨ B) ∧ (A ∨ C). Along the way, you’ll see how complement identities like X' ∨ X = 1 and B ∨ B' = 1 help collapse big formulas into small, elegant ones. By the end, turning a cluttered expression into a neat, equivalent version will start to feel natural. see less

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) Simplify ¬(A ∨ B)

Explanation

According to De Morgan's law, the negation of a disjunction is the conjunction of the negations. Therefore, ¬(A ∨ B) is equivalent to ¬A ∧ ¬B.

Submit
3) Simplify ¬(A' ∧ B')

Explanation

Apply De Morgan's law: ¬(A' ∧ B') = ¬A' ∨ ¬B'. Since ¬A' is A and ¬B' is B, this simplifies to A ∨ B.

Submit
4) Simplify ¬(¬A ∨ ¬B)

Explanation

Apply De Morgan's law: ¬(¬A ∨ ¬B) = ¬¬A ∧ ¬¬B. Since ¬¬A is A and ¬¬B is B, this simplifies to A ∧ B.

Submit
5) Simplify ¬(A' ∨ B)

Explanation

Apply De Morgan's law: ¬(A' ∨ B) = ¬A' ∧ ¬B. Since ¬A' is A, this simplifies to A ∧ ¬B.

Submit
6) (A ∧ B)' V (A ∧ B)

Explanation

This expression is of the form X' ∨ X, where X is (A ∧ B). According to the complement law, X' ∨ X = 1 for any X. Therefore, (A ∧ B)' ∨ (A ∧ B) = 1.
Submit
7) Simplify A ∧ (B V C)

Explanation

According to the distributive law of conjunction over disjunction, A ∧ (B V C) is equivalent to (A ∧ B) V (A ∧ C).

Submit
8) Simplify A V (B ∧ C)

Explanation

According to the distributive law of disjunction over conjunction, A V (B ∧ C) is equivalent to (A V B) ∧ (A V C).

Submit
9) Simplify (A ∧ B) V (A ∧ C)

Explanation

According to the distributive law, (A ∧ B) V (A ∧ C) can be factored as A ∧ (B V C).
Submit
10) Simplify (A V B) ∧ (A V C)

Explanation

According to the distributive law, (A V B) ∧ (A V C) can be simplified to A V (B ∧ C).
Submit
11) Simplify (A ∧ B) ∨ (A ∧ B')

Explanation

Factor out A: (A ∧ B) ∨ (A ∧ B') = A ∧ (B ∨ B'). Since B ∨ B' = 1 by complement law, then A ∧ 1 = A by identity law.
Submit
12) Simplify A ∧ B ∧ (A ∨ C)

Explanation

According to the absorption law, A ∧ B ∧ (A ∨ C) simplifies to A ∧ B. This is because if A and B are true, the expression is true regardless of C, and if A or B is false, the expression is false.
Submit
13) Simplify (A ∨ B) ∧ A

Explanation

According to the absorption law, (A ∨ B) ∧ A simplifies to A. This can be seen by distribution: (A ∨ B) ∧ A = A ∧ A ∨ B ∧ A = A ∨ (A ∧ B) = A by absorption. 

Submit
14) Simplify (A ∨ B) ∧ (A ∨ B)

Explanation

According to the idempotent law, the conjunction of an expression with itself is the expression itself. Therefore, (A ∨ B) ∧ (A ∨ B) = A ∨ B.
Submit
15) Simplify A ∨ (A' ∧ B)

Explanation

Using the distributive law, A ∨ (A' ∧ B) = (A ∨ A') ∧ (A ∨ B) = 1 ∧ (A ∨ B) = A ∨ B by identity law.
Submit
×
Saved
Thank you for your feedback!
15)
Your input helps us improve, and you’ll get your detailed results next.
View My Results
Cancel
  • All
    All (15)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Simplify ¬(A ∧ B)
Simplify ¬(A ∨ B)
Simplify ¬(A' ∧ B')
Simplify ¬(¬A ∨ ¬B)
Simplify ¬(A' ∨ B)
(A ∧ B)' V (A ∧ B)
Simplify A ∧ (B V C)
Simplify A V (B ∧ C)
Simplify (A ∧ B) V (A ∧ C)
Simplify (A V B) ∧ (A V C)
Simplify (A ∧ B) ∨ (A ∧ B')
Simplify A ∧ B ∧ (A ∨ C)
Simplify (A ∨ B) ∧ A
Simplify (A ∨ B) ∧ (A ∨ B)
Simplify A ∨ (A' ∧ B)
Alert!

Advertisement