**(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

Therefore $A\subset B.$

*A*is an element of set*B*.Therefore $A\subset B.$

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

3.

3.

**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

**2**.

^{n} For example, if

*A*= {3, 7} So

*n*= 2, then number of subsets of set*A*= 2^{2}= 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:

Example:

If ξ = {17, 18, 19, 20, 21, 22, 23} and

*B*= {17, 20, 21} then

*B*’ = {18, 19, 22, 23}

**. The Venn diagram below shows the relationship between**

2

2

*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*.