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:
A = {1, 3, 5, 7, 9}
4. In set notation, the symbol
∈
means ‘is an element of’ or ‘belongs to’ and
∉
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
∈or∉
, 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)5∈P←5is an element of setP(b) 20∉P←20 is not an element of setP(c) 25∈Q←25is an element of setQ(d) 8∉Q←8 is not an element of setQ
(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 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.