# 11.2.2 Venn Diagram, Universal Sets, Complement of a Set and Subset (2)

(B) Subsets
1. If every element of a set A is also an element of a set B, then set A is called subset of set B.

2. The symbol ⊂ is used to denote ‘is a subset of’.
Therefore, set A is a subset of set B. In set notation, it is written as A ⊂ B.
Example:
A = {11, 12, 13} and B = {10, 11, 12, 13, 14}
Every element of set A is an element of set B.
Therefore  $A\subset B.$

3.

$A\subset B.$  can be illustrated using Venn diagram as below:

4. The symbol   $\not\subset$ is used to denote ‘is not a subset of’.

5. An empty set is a subset of any set.
For example, $\varnothing \subset A$

6. A set is a subset of itself.
For example,   $B\subset B$

7. The number of subsets for a set with n elements is 2n.
For example, if A = {3, 7}
So n = 2, then number of subsets of set A = 22 = 4
All the subsets of set A are { }, {3}, {7} and {3, 7}.

(C) Complement of a Set
1. The complement of set B is the set of all elements in the universal set, ξ, which are not elements of set B, and is denoted by B’.

Example:
If ξ = {17, 18, 19, 20, 21, 22, 23} and
B = {17, 20, 21} then
B’ = {18, 19, 22, 23}

2
. The Venn diagram below shows the relationship between B, B’ and the universal set, ξ.

The complement of set B is represented by the green colour shaded region inside the universal set, ξ, but outside set B.