Page 19 - Math 7

Set

Worked-out examples

Example 1: If M = {m, a, t, h, s} and N = {m, a, g, i, c}, find
(a) M ‰ N (b) M ˆ N (c) M – N, (d) N – M. Also, represent them in
Venn diagrams.
Solution:
Here, M = {m, a, t, h, s} and N = {m, a, g, i, c} M N
Now, t m g
h i
a) M ‰ N = {m, a, t, h, s} ‰ {m, a, g, i, c} = {m, a, t, h, s, g, i, c} a c
s
The shaded region represents M ‰ N. M N

t m g
b) M ˆ N = {m, a, t, h, s} ˆ {m, a, g, i, c} = {m, a} h i
a
s c
The shaded region represents M ˆ N.
M N
t m g
c) M – N = {m, a, t, h, s} – {m, a, g, i, c} = {t, h, s}
h i
a
s c
The shaded region represents M – N.
M N
d) N – M = {m, a, g, i, c} – {m, a, t, h, s} = {g, i, c} t m g
h i
a c
The shaded region represents N – M. s

Example 2: If U = {0, 1, 2, …, 10}, A = {1, 2, 3, 4, 5}, and B = {1, 3, 5, 7, 9},
complete the following set operations and represent them in
Venn-diagrams.
a) A ‰ B b) A ˆ B c) A – B d) B – A
e) A ‰ B f) A ˆ B g) A – B h) B – A
Solution:
Here, U = {0, 1, 2, …, 10}, A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7, 9}
U
Now, A B
2 1 7
a) A ‰ B = {1, 2, 3, 4, 5} ‰ {1, 3, 5, 7, 9} and 0 3
4 5 9
B = {1, 2, 3, 5, 7, 9} 6 8 10
U
The shaded region represents A ‰ B.
A B
2 1
0 3 7
b) A ˆ B = {1, 2, 3, 4, 5} ˆ {1, 3, 5, 7, 9} = {1, 3, 5} 4 5
The shaded region represents A ˆ B. 6 8 9 10

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 17 Vedanta Excel in Mathematics - Book 7