+2 Math Formulas
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www.mathportal.org Algebra Formulas 1. Set identities Definitions: I: Universal set A’: Complement Empty set: ∅ Union of sets { } | A B x x x B r A o ∪ = ∈ ∈ Intersection of sets { } | A B x x x B d A an ∩ = ∈ ∈ Complement { } | A x I x A ′ = ∈ ∈ Difference of sets { } \ | B A x x B x A and = ∈ ∉ Cartesian product ( ) { } , | A B x y x A and y B × = ∈ ∈ Set identities involving union Commutativity A B B A ∪ = ∪ Associativity ( ) ( ) A B C A B C ∪ ∪ = ∪ ∪ Idempotency A A A ∪ = Set identities involving intersection commutativity A B B A ∩ = ∩ Associativity ( ) ( ) A B C A B C ∩ ∩ = ∩ ∩ Idempotency A A A ∩ = Set identities involving union and intersection Distributivity ( ) ( ) ( ) A B C A B A C ∪ ∩ = ∪ ∩ ∪ ( ) ( ) ( ) A B C A B A C ∩ ∪ = ∩ ∪ ∩ Domination A ∩∅ = ∅ A I I ∪ = Identity A A ∪ ∅ = A I A ∩ = Set identities involving union, intersection and complement complement of intersection and union A A I ′ ∪ = A A′ ∩ = ∅ De Morgan’s laws ( ) A B A B ′ ′ ′ ∪ = ∩ ( ) A B A B ′ ′ ′ ∩ = ∪ Set identities involving difference ( ) \ B A B A B = ∪ \ B A B A′ = ∩ \ A A = ∅ ( ) ( ) ( ) \ \ A B C A C B C ∩ = ∩ ∩ \ A I A ′ = 2. Sets of Numbers Definitions: N: Natural numbers N o : Whole numbers Z: Integers Z + : Positive integers Z - : Negative integers Q: Rational numbers C: Complex numbers Natural numbers (counting numbers ) { } 1 , 2, 3,... N = Whole numbers ( counting numbers + zero ) { } 0, 1, 2, 3,... o N = Integers { } 1, 2, 3,... Z N + = = { } ..., 3, 2, 1 Z − = − − − { } { } 0 . .., 3 , 2 , 1 , 0, 1 , 2 , 3 ,... Z Z Z − = ∪ ∪ = − − −
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