Question

What is the number of proper subsets of a given
finite set with n elements?

Answer 1

( number of sets) - 1 = number of proper set...
and the -1 because the set is not himselfs proper set...
I hope you can understand...

Answer 2

Obviously,every set is the subset of itself and the void set ∅∅ is the subset of every set. These two subsets are called improper subsets.

It also includes a theorem which states that "Let A be a finite set having n elements. Then the total number of subsets of A is (2n2n) and the number of proper subsets of A is (2n−1).2n−1)."

Then again in a sample solution of this problem "If A = {a,b,c},then the number of proper subsets of A is ?"

Total no of subsets of {a,b,c} = 2323 = 8. But each set have two improper subset, so number of improper subsets are 6.

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