Discussion
The number of non-empty proper subsets of X = {1, 2, 3, 4, 5} is :
Answer: D
There are 30 non-empty proper subsets.
A set with 5 elements has \(2^{5} = 32\) subsets in all. A proper subset excludes X itself, and non-empty excludes \(\varnothing\), so
\[ 2^{5} - 2 = 30 \]
31 removes only one of the two (either the empty set or X), 32 counts every subset, and 16 is \(2^{4}\), the number of subsets of a four-element set.
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