Question

Find the number of subsets and the number of proper subsets of the following set

X = {x² : x ∈ N, x² ≤ 100}

Answer 1

X = {x² : x ∈ N, x² ≤ 100}

X = {1, 2, 3, 4, …. 10}

n(X) = 10

The number of subsets of X

= n[P(X)]

= 2^m

= 2¹⁰

= 1024

Number of proper subsets of X

= 2^m – 1

= 1024 – 1

= 1023