Definition

A Venn diagram is a rectangular shape drawn to enclose all the sets in the universal set

Subsets

A set is a subset of another if its elements are obtained from the other set. Subset is denoted by ⊂ . If A is a subset of B, then it can be represented on a Venn diagram as shown below;

                                                                           ε

                            A⊂B

Intersection

The intersection of 2 sets A and B can be represented on a Venn diagram as follows

                                                                                    ε

                            A∩B = shaded region

Union

                                                                                      ε

                     A∪B = shaded region

Complement of a set

Given the set A, its complement can be represented on a Venn diagram as shown below;

                                                                             ε

A^C = is the coloured region

Ex: If A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7}. Show on a Venn diagram the following;

a) A∩B, b) A∪B, c) the universal set ε, d) (A∩B)^I

Solution:

a) A∩B = {1, 3, 5}  b) A∪B = {1, 2, 3, 4, 5, 7}  c) ε = {1, 2, 3, 4, 5, 7}  d) (A∩B)^I = {2, 4, 7}