# 3.1 Set

3.1 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:
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}

$\begin{array}{l}\text{(a)}5\text{}\in P\text{}←\overline{)\text{}5\text{is an element of set}P\text{}}\\ \text{(b) 20}\notin \text{}P\text{}←\overline{)\text{20 is not an element of set}P\text{}}\\ \text{(c) 2}5\text{}\in Q\text{}←\overline{)\text{2}5\text{is an element of set}Q\text{}}\\ \text{(d) 8}\notin \text{}Q\text{}←\overline{)\text{8 is not an element of set}Q\text{}}\end{array}$

(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.
6. A dot to the left of an object in a Venn diagram indicates that the object is an element of the set.
7. When a Venn diagram represents the 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 Aφ 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.