Venn Diagram
use to show relationships between items
Set Operations (Union & Intersection)
A∪B={x ∣ x∈A or x∈B} : Union
A∩B={x ∣ x∈A and x∈B} : Intersection
e.g. A={1,2,3,4}, B={3,4,5,6}, then, A∪B={1,2,3,4,5,6}, A∩B={3,4}
Properties of Union and Intersection
A∪B=B∪A, A∩B=B∩A : Commutative Law
(A∪B)∪C=A∪(B∪C), (A∩B)∩C=A∩(B∩C) : Associative Law
A∪(B∩C)=(A∪B)∩(A∪C), A∩(B∪C)=(A∩B)∪(A∩C) : Distributive Law
A∪{}=A, A∩{}={}
A∪U=U
A∪A=A,A∩A=A : Idempotent Law