Laws of Set Theory Flashcards
1
Q
Definition of Set Equality
A
A \subseteq B and B \subseteq A
2
Q
A U B
A
(x in A) or (x in B)
3
Q
A n B
A
(x in A) and (x in B)
4
Q
A oplus B (‘x in’ notation)
A
(x in A\B) or (x in B\A)
5
Q
A oplus B (intersect and union)
A
(A U B) \ (A n B)
6
Q
A \ B (‘x in’ notation)
A
(x in A) and (x not in B)
7
Q
A \ B (complement notation)
A
A U B^c
8
Q
A^c
A
U \ A
9
Q
Law of Commutativity
A
A U B = B U A, A = B \LE B = A
10
Q
Law of Associativity
A
A U (B U C) = (A U B) U C
11
Q
Law of Distributivity
A
A n (B U C) = (A n B) U (A n C)
(A n B) U C = (A U C) n (B U C)
12
Q
Double Complement
A
(A^c)^c = A
13
Q
De Morgan’s Law
A
(A U B)^c = A^c n B^c
(A n B)^c = A^c U B^c
14
Q
Identity Law
A
A U \emptyset = A
A n \mathbb{U} = A
15
Q
Idempotence
A
