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Question
Find the number of subsets and the number of proper subsets of the following set
X = {x² : x ∈ N, x² ≤ 100}
Solution
X = {x2 : x ∈ N, x2 ≤ 100}
X = {1, 2, 3, 4, …. 10}
n(X) = 10
The number of subsets of X
= n[P(X)]
= 2m
= 210
= 1024
Number of proper subsets of X
= 2m – 1
= 1024 – 1
= 1023
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