Compound Statements & Equivalences

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: 7288 | Total Attempts: 9,526,515
| Questions: 10 | Updated: Nov 12, 2025
Please wait...
Question 1 / 10
0 %
0/100
Score 0/100
1) (p ∧ q) ∨ r for p = T, q = F, r = T.

Explanation

p ∧ q = F; F ∨ T = T.

Submit
Please wait...
About This Quiz
Compound Statements & Equivalences - Quiz

Logic can be built piece by piece! In this quiz, you’ll explore compound statements, test for equivalences, and see how different logical expressions connect. Try this quiz to sharpen your reasoning step by step.

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) (p ∨ q) ∧ r for p = F, q = T, r = F.

Explanation

p ∨ q = T; T ∧ F = F.

Submit
3) ¬(p ∧ q) for p = T, q = T.

Explanation

p ∧ q = T; negation gives F.

Submit
4) ¬(p ∧ q) for p = T, q = F.

Explanation

p ∧ q = F; negation gives T.

Submit
5) (p ∨ q) ∨ ¬(p ∧ q) for p = F, q = F.

Explanation

p ∨ q = F; p ∧ q = F; ¬F = T; F ∨ T = T.

Submit
6) (p ∨ q) ∧ ¬(p ∧ q) for p = T, q = T.

Explanation

p ∨ q = T; p ∧ q = T; ¬T = F; T ∧ F = F.

Submit
7) (p ∨ q) ∧ ¬(p ∧ q) for p = T, q = F.

Explanation

p ∨ q = T; p ∧ q = F; ¬F = T; T ∧ T = T.

Submit
8) ¬p ∧ (p ∨ q) for p = F, q = T.

Explanation

¬p = T; p ∨ q = T; T ∧ T = T.

Submit
9) ¬p ∧ (p ∨ q) for p = T, q = F.

Explanation

¬p = F; p ∨ q = T; F ∧ T = F.

Submit
10) (p ∧ q) ∨ (¬p ∧ ¬q) for p = F, q = F.

Explanation

p ∧ q = F; ¬p = T, ¬q = T; T ∧ T = T; F ∨ T = T.

Submit
×
Saved
Thank you for your feedback!
10)
Your input helps us improve, and you’ll get your detailed results next.
View My Results
Cancel
  • All
    All (10)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
(p ∧ q) ∨ r for p = T, q = F, r = T.
(p ∨ q) ∧ r for p = F, q = T, r = F.
¬(p ∧ q) for p = T, q = T.
¬(p ∧ q) for p = T, q = F.
(p ∨ q) ∨ ¬(p ∧ q) for p = F, q = F.
(p ∨ q) ∧ ¬(p ∧ q) for p = T, q = T.
(p ∨ q) ∧ ¬(p ∧ q) for p = T, q = F.
¬p ∧ (p ∨ q) for p = F, q = T.
¬p ∧ (p ∨ q) for p = T, q = F.
(p ∧ q) ∨ (¬p ∧ ¬q) for p = F, q = F.
Alert!

Advertisement