Venn Diagrams and DeMorgan's Laws

Universal Set -> U

Set A-> A

Not A -> !A -> Complement of A

Set B -> B

Not B -> !B -> Complement of B

A and B -> A && B -> A intersect B

Not (A and B) -> ! (A && B) -> Complement of (A intersect B)

A or B -> A || B -> A union B

Not (A or B) -> ! (A || B) -> Complement of (A union B)

(Not A) or (Not B) -> (!A) || (!B) -> union of (Complement of A) and (Complement of B)

(Not A) and (Not B) -> (!A) && (!B) -> intersection of (Complement of A) and (Complement of B)

DeMorgan's Law 1: !(A && B) == (!A) || (!B) -> Complement of (A intersect B) == union of (Complement of A) and (Complement of B)

DeMorgan's Law 2: !(A || B) == (!A) && (!B) -> Complement of (A union B) == intersection of (Complement of A) and (Complement of B)