Verified answer

Solution :

(i) If A = {p, q, r},

Number of elements in A = 3

Then number of subsets of A=2^3=2\times2\times2=82

3

=2×2×2=8

Therefore, the number of proper subset of A is 8.

(ii) If B = {5, 4, 6, 8}

Number of elements in B = 4

Then number of subsets of B

= 2^4-1=2\times2\times2\times2-12

4

−1=2×2×2×2−1

=16-1=1516−1=15

Therefore, the number of proper subset of B is 15.

(iii) If C = {0},

Number of elements in C = 1

then number of subsets of C =2^1=22

1

=2

Therefore, the number of proper subset of C is 2.

(iv) If M = {x: x ∈ N and x < 3}, = {1, 2}

Number of elements in M = 2

Then number of subsets of M = 2^2-1=4-1=32

2

−1=4−1=3

Therefore, the number of proper subset of M is 3.