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Math #1

all of math

TermDefinition
Proposition A logical statement
Implication False if I lie / If ... Then ...
Biconditional True when both are true/false
Tautology All true
Contradiction All false
Converse q → p is the converse of p → q
Inverse ¬p → ¬q is the inverse of p → q
Contrapositive ¬q → ¬p is the contrapositive of p → q
Demorgan's law Flip "and/or," negate terms. ¬(p ∨ q) ≡ ¬p ∧ ¬q. NOT (rich or famous) = NOT rich AND NOT famous
Identity laws Combining a value with True for "and" or False for "or" doesn't change the value. p ∨ F ≡ p, p ∧ T ≡ p
Domination laws True dominates "or", false dominates "and". p ∨ T ≡ T , p ∧ F ≡ F
Idempotent laws Repeating a value doesn't change it. p ∨ p ≡ p , p ∧ p ≡ p
Double Negation laws Not-not equals itself. ¬(¬p) ≡ p
Negation laws A value and its opposite(not) cancel each other out. p ∨ ¬p ≡ T, p ∧ ¬p ≡ F
Commutative laws Order doesn't matter for "and/or". p ∨ q ≡ q ∨ p, p ∧ q ≡ q ∧ p
Distributive laws Factor terms across "and/or". (p ∨ (q ∧ r)) ≡ (p ∨ q) ∧ (p ∨ r), (p ∧ (q ∨ r)) ≡ (p ∧ q) ∨ (p ∧ r)
Absorption laws A term combined with itself under "or" / "and" simplifies to itself. p ∨ (p ∧ q) ≡ p, p ∧ (p ∨ q) ≡ p
Created by: jolly_n4
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