__4.1 Set__**1.**A set is a collection of objects according to certain characteristics

**2.**The

**objects**in a set are known as

**elements**.

**3.**Sets are usually denoted by

**capital letters**and notation used for sets is

**braces**,

**{ }**.

Example:

Example:

*A*= {1, 3, 5, 7, 9}

**4.**In set notation, the symbol $\in $ means

**‘is an element of’**or

**‘belongs to’**and $\notin $ means

**‘is not an element of’**or

**‘does not belong to’**.

**Example 1:**

Given that

*P*= {factors of 15} and*Q*= {positive perfect squares less than 28}. By using the symbol $\in \text{or}\notin $ , complete each of the following:**(a)**5 ___

*P*

**(b)**20 ___

*P*

**(c)**25 ___

*Q*

**(d)**8 ___

*Q*

*Solution:**P*= {1, 3, 5, 15},

*Q*= {1, 4, 9, 16, 25}

**(A) Represent sets by using Venn diagram**

**5.**A set can be represented by a

**Venn diagram**using closed geometry shapes such as circles, rectangles, triangles and etc.

**A**

6.

6.

**dot to the left**of an object in a Venn diagram indicates that the object is an

**element**of the set.

**When a Venn diagram represents the**

7.

7.

**number**of elements in a set,

**no dot**is placed to the left of the number.

**Example 2:**

**(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

**(B) Determine whether a set is an empty set**

**8.**A set with

**no elements**is called an

**empty set**or

**null set**. The symbol φ or

**empty braces, { }**, denotes empty set.

For example, if set

*A*is an empty set, then*A*= { } or*A*= φ and*n*(

*A*) = 0.

**9.**If

*B*= {0} or {φ} does not denote that

*B*is an empty set.

*B*= {0} means that there is an element ‘0’ in set

*B*.

*B*= {φ} means that there is an element ‘φ’ in set

*B*.