# Chapter 2 - Set Theory - 2.2 Subsets - Exercise Set 2.2: 68

Total number of proper subsets are 31

#### Work Step by Step

{X|X ∈ N and 2≤X≤6} = {2,3,4,5,6} A set of n elements have 2^{n} number of subsets. Here set has 5 elements. So total number of subsets are 2^{5}=32 As these 8 subsets also include the one subset which is the set itself. We need to exclude this one subset. Thus Total number of proper subsets are = 32 - 1 = 31

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