Compound Statements & Equivalences

  • 11th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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By Thames
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Thames
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Attempts: 11 | Questions: 10 | Updated: Jan 21, 2026
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Question 1 / 11
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1) (p ∧ q) ∨ r for p = T, q = F, r = T.

Explanation

p ∧ q = F; F ∨ T = T.

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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.

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2) (p ∨ q) ∧ r for p = F, q = T, r = F.

Explanation

p ∨ q = T; T ∧ F = F.

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3) ¬(p ∧ q) for p = T, q = T.

Explanation

p ∧ q = T; negation gives F.

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4) ¬(p ∧ q) for p = T, q = F.

Explanation

p ∧ q = F; negation gives T.

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

Explanation

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

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

Explanation

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

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

Explanation

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

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8) ¬p ∧ (p ∨ q) for p = F, q = T.

Explanation

¬p = T; p ∨ q = T; T ∧ T = T.

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9) ¬p ∧ (p ∨ q) for p = T, q = F.

Explanation

¬p = F; p ∨ q = T; F ∧ T = F.

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

Explanation

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

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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(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.
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