WGU C959 Logical Equivalences (Laws)

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Last updated 3:34 PM on 7/31/26
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12 Terms

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Identity

p ∨ F ≡ p

p ∧ T ≡ p

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Domination

p ∨ T ≡ T

p ∧ F ≡ F

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Idempotent

p ∨ p ≡ p

p ∧ p ≡ p

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Double Negation

¬(¬p) ≡ p

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Commutative

p ∨ q ≡ q ∨ p

p ∧ q ≡ q ∧ p

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Associative

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

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Distributive

p ∨ (q ∧ r) ≡ (p∨q) ∧ (p∨r)

p ∧ (q ∨ r) ≡ (p∧q) ∨ (p∧r)

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De Morgan’s

¬(p ∨ q) ≡ ¬p ∧ ¬q

¬(p ∧ q) ≡ ¬p ∨ ¬q

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Absorption

p ∨ (p ∧ q) ≡ p

p ∧ (p ∨ q) ≡ p

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Complement

p ∨ ¬p ≡ T

p ∧ ¬p ≡ F

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Conditional

p → q ≡ ¬p ∨ q

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Biconditional

p ↔ q ≡ (p → q) ∧ (q → p)