discrete math

converse : the statement formed by exchanging the hypothesis and conclusion of an implication

inverse : If not p, then not q

Double Negation Law : ¬(¬p) ≡ p

Commutative Law : p ∨ q ≡ q ∨ pp ∧ q ≡ q ∧ p

negation laws : p ∨ ¬p ≡ Tp ∧ ¬p ≡ F

p → q : p → q ≡ ¬p ∨ qp → q ≡ ¬q → ¬p

p ↔︎ q : (p → q) ∧ (q → p)¬p ↔︎ ¬q(p ∧ q) ∨ (¬p ∧ ¬q)

De Morgan's law for quantified statements : ¬∀x P(x) ≡ ∃x ¬P(x)¬∃x P(x) ≡ ∀x ¬P(x)

inference:- addition- simplification- conjunction- resolution :

Fallacy of Affirming the Conclusion : ((p → q) ∧ q) → p

deduction theorem :

set difference distribution :

asymmetric : (a,b) and not (b,a)asymmetric implies antisymmetric (vacuously)

antisymmetric : (a,b) and (b,a) -> a=b

congruence modulo : x \equiv y (mod n) -> [x] = {x + kn | k \in Z}

partial order relation : reflexive, antisymmetric, transitive

injective : describes a mapping in which each element of the domain maps to a single element of the range. Also, one-to-one.

surjective : describes a mapping in which each element of the range is the target of some element of the domain. Also, onto.