Discrete Math Terms & Definitions for Key Laws

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16 Terms

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DeMorgan's Laws

¬(p ∧ q) == ¬p ∨ ¬q

¬(p ∨ q) == ¬p ∧ ¬q

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Double Negation Law

¬[¬p] == p

3
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Implication Law

p → q == ¬p ∨ q

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Contrapositive

p → q == ¬q → ¬p

5
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Negation of Implication

¬(p → q) == p ∧ ¬q

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Identity Laws

p ∨ F == p

p ∧ T == p

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Commutative Laws

p ∨ q == q ∨ p

p ∧ q == q ∧ p

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Associative Laws

(p ∨ q) ∨ r == p ∨ (q ∨ r)

(p ∧ q) ∧ r == p ∧ (q ∧ r)

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Distributive Laws

p ∧ (q ∨ r) == (p ∧ q) ∨ (p ∧ r)

p ∨ (q ∧ r) == (p ∨ q) ∧ (p ∨ r)

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Domination Laws

p ∨ T == T

p ∧ F == F

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Idempotent Laws

p ∨ p == p

p ∧ p == p

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Absorption Laws

p ∧ (p ∨ q) == p

p ∨ (p ∧ q) == p

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Tautology

p ∨ ¬p == T

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Contradiction

p ∧ ¬p == F

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Equivalence

(p → q) ∧ (q → p) == (p ↔ q)

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Universal Instantiation

∀xP(x)

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P(c)