Set intersection

Intersection of sets A and B is a set C which contains elements that belong both to A and B.

Intersection is represented by such a diagram:

Denoted: C = A B.

Intersection consists of the domains that have darker shading.

C = A B = {x │ x A and x B}.

Ex.: A = {0, 1, 2, 3}, B = {0, 2, 4, 6}, C = {0, 2}.

Using the notion of the universal set one can define the operation of the compliment of a set.

A universal set contains all elements that are of interest to us.

Set compliment

A compliment of a set A is a set B that contains all the elements of the universal set that does not belong to A.

Compliment is represented by such a diagram:

Denoted Ā

Compliment consists of the domain without shading.

Ā = {x │ x U and x A}.

Ex.: U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 2, 4, 6, 8}, Ā = {1, 3, 5, 7, 9}, where universal set is a set of decimal digits, A is a set of even digits and Ā consists of odd digits.