**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.

**A**

2.

2.

**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**

3.

3.

**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:

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:Solution:

**(a)**

ξ = {0, 1, 2, 3, 4, 5, 6, 7, 8}

*A*= {2, 3, 5, 7}

*B*= {4, 8}

**(b)(i)**

**(b)(ii)**