MASTERED - Basic Logical Identities - Discrete Math

ANYTHING IS POSSIBLEEEEEE - LEGOAT

Identity Laws

p ^ T ≡ p

p v F ≡ p

Domination Laws

p v T ≡ T

p ^ F ≡ F

How the T/F affects P

Idempotent Laws

p V p ≡ p

p ^ p ≡ p

Double Negative Laws

¬(¬p) ≡ p

Communicative Laws

p V q ≡ q V p

p ^ q ≡ q ^ p

Flip the letters ONLY

Associative Laws

(p V q) V r ≡ p V (q V r)

(p ^ q) ^ r ≡ p ^ (q ^ r)

Moving over the Parentheses

Distributive Laws

p V (q ^ r) ≡ (p V q) ^ (p V r)

p ^ (q V r) ≡ (p ^ q) V (p ^ r)

Distributing + Alternating Signs

De Morgan’s Laws

¬(p ^ q) ≡ ¬p V ¬q

¬(p V q) ≡ ¬p ^ ¬q

Opps Everywhere!

Negation Laws

p V ¬p ≡ T

p ^ ¬p ≡ F

Conditional Law

p → q ≡ ¬p V q

Tricky Squirrel

Biconditional Law

p ↔ q ≡ (p → q) ^ (q → p)

Common Sense EZPZ.