Intersection of Sets – Sets

Consider again the example of cricket team and hockey team of your school where three players, say Ram, John and Ismail are playing in both the teams. Suppose the school wants to felicitate players who plays for both the teams. What will be the set of all players who felicitated? It will be the set C = {Ram, John, Ismail}.Suppose we denote the set of all cricket players by A and the set of all hockey players by B. Then C is precisely the set of all players who are both in set A and set B. Thus

C = {x : x ∈A and x ∈B}

Given two sets A and B their intersection is the set of all those elements which are both in A and B. This is denoted by A∩B (read as A intersection B). Thus, A∩B = {x |x ∈A and x ∈B}.

Example : Let A = {1,2, 3, 4} and B = {2, 4, 5, 6} Find A∩B.

Solution:

Note that only common elements of A and B are {2, 4}. Hence A∩B = {2, 4}In the adjecent Venn diagram, the shaded portion represent A∩B.

Observe that A∩B = B∩A. Thus intersection is a commutative operation.

Two sets A and B are disjoint if and only if A∩B = ∅.