Page 14 - Math 7

Set

Thus, the set B is said to be an improper subset of A, if B is equal to A, i.e., B = A. We
use the symbol Ž to represent a set as an improper subset of another set. For example,
B Ž A and we read it as 'B is an improper subset of A'.
Number of subsets of a given set

Let's study the following table and draw the conclusion about the number of subsets
of a given set.
Set Subsets No. of elements No. of subsets
A = { } { } n(A) = 0 1 m 2°
B = {a} {a}, I n(B) = 1 2 m 2 1
C = {a, b} {a}, {b}, {a, b}, I n(C) = 2 4 m 2 2
D = {a, b, c} {a}, {b}, {c}, {a, b}, 3
{b, c}, {a, c} {a, b, c} I n(D) = 3 8 m 2

From the above table, we conclude that the number of subsets of a set is given by the
formula 2 , where n is the cardinal number of the given set.
n
EXERCISE 1.2

General section - Classwork
1. Let's say whether these pairs of sets are equal or equivalent sets and write
A = B or A ~ B in the blank spaces.

(a) A = {1, 2, 4, 8 } and B = { 1, 4, 9, 16}, .......................................
(b) A = { 4, 6, 8, 9, 10} and B = { 6, 9, 4, 8, 10}, ......................................

2. Let's say and write whether these pairs of sets are overlapping or disjoint sets.

(a) A = { 1, 3, 5, 15 } and B = {5, 10, 15, 20}, A and B are .........................

(b) P = { 1, 3, 5, 7, 9 } and Q = { 4, 8, 12 }, P and Q are ........................
3. Let's say and fill in the blanks with appropriate words.
(a) If each element of set A is also an element of B, A is said to be
a ............................... of B and B is said to be a ............................... of A.
(b) Every set is a ............................... of itself.
(c) The empty set is a ............................... of every set.

(d) The number of possible subsets of a set containing 'n' number of elements
is given by the formula ...............................
4. Let's say and write the possible number of subsets of these sets.
(a) In {1, 2}, number of subsets = .................................................................
(b) In {g, o, d }, number of subsets = .................................................................

Vedanta Excel in Mathematics - Book 7 12 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur