Intersection (set Theory) - Basic Definition

Basic Definition

The intersection of A and B is written "A ∩ B". Formally:

that is

x ∈ A ∩ B if and only if

• x ∈ A and
• x ∈ B.

For example:

• The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
• The number 9 is not in the intersection of the set of prime numbers {2, 3, 5, 7, 11, …} and the set of odd numbers {1, 3, 5, 7, 9, 11, …}.

More generally, one can take the intersection of several sets at once. The intersection of A, B, C, and D, for example, is A ∩ B ∩ C ∩ D = A ∩ (B ∩ (C ∩ D)). Intersection is an associative operation; thus,
A ∩ (B ∩ C) = (A ∩ B) ∩ C.

If the sets A and B are closed under complement then the intersection of A and B may be written as the complement of the union of their complements, derived easily from De Morgan's laws:
A ∩ B = (Ac ∪ Bc)c