Find the number of subsets and the number of proper subsets of the fol

1.	Find the number of subsets and the number of proper subsets of the following sets.(i) W = {red,blue, yellow}(ii) X = {x2 : x ∈ N, x2 ≤ 100}.
Answer» (i) Given W = {red, blue, yellow} Then n(W) = 3 The number of subsets = n[P(W)] = 2³ = 8 The number of proper subsets = n[P(W)] – 1 = 2³ – 1 = 8 – 1 = 7 (ii) Given X = {1,2,3, } X² = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} n(X) = 10 The Number of subsets = n[P(X)] = 2¹⁰ = 1024 The Number of proper subsets = n[P(X)] – 1 = 2¹⁰ – 1 = 1024 – 1 = 1023.

Find the number of subsets and the number of proper subsets of the following sets.(i) W = {red,blue, yellow}(ii) X = {x2 : x ∈ N, x2 ≤ 100}.

Answer»

(i) Given W = {red, blue, yellow}

Then n(W) = 3

The number of subsets = n[P(W)] = 2³ = 8

The number of proper subsets = n[P(W)] – 1 = 2³ – 1 = 8 – 1

= 7

(ii) Given X = {1,2,3, }

X² = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

n(X) = 10

The Number of subsets = n[P(X)] = 2¹⁰ = 1024

The Number of proper subsets = n[P(X)] – 1 = 2¹⁰ – 1 = 1024 – 1

= 1023.