# 11.2.1 Venn Diagram, Universal Sets, Complement of a Set and Subset (1)

Universal Set
1. Universal set is a set that contains all the elements under consideration.
2. In set notation, the symbol ξ denotes a universal set.
3. All the other sets are subset to the universal set.

(A) Represent sets by using Venn diagram
1. A set can be represented by a Venn diagram using closed geometry shapes such as circles, rectangles, triangles and etc.

2.
A dot to the left of an object in a Venn diagram indicates that the object is an element of the set.

3.
When a Venn diagram represents the number of elements in a set, no dot is placed to the left of the number.

Example 1:
(a) Draw a Venn diagram to represent each of the following sets.
(b) State the number of elements for each of the set.
A= {2, 3, 5, 7}
B= {k, m, r, t, y}

Solution:
(a)
(b)
n(A) = 4
n(B) = 5

Example 2:
Given that the universal set, ξ = {whole numbers less than 9}, A = {prime number} and B = {multiple of 4}.
(a) List all the elements of set A and set B.
(b) Illustrate the relationships between the following sets using Venn diagrams.
(i) ξ and A
(ii) ξ, A and B

Solution:
(a)
ξ = {0, 1, 2, 3, 4, 5, 6, 7, 8}
A = {2, 3, 5, 7}
B = {4, 8}

(b)(i)

(b)(ii)