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.
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.
2. A dot to the left of an object in a Venn diagram indicates that the object is an element of the set.
3. When a Venn diagram represents the 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:
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:
(a)
ξ = {0, 1, 2, 3, 4, 5, 6, 7, 8}
ξ = {0, 1, 2, 3, 4, 5, 6, 7, 8}
A = {2, 3, 5, 7}
B = {4, 8}
(b)(i)
(b)(ii)
