Compound Statements & Equivalences

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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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  • Oct 13, 2025
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  • Oct 07, 2025
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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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