Answers:
128 subsets
127 proper subsets
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Explanation:
Set P is the set of letters from the word "PREPOSTEROUS"
So P = {P,R,E,P,O,S,T,E,R,O,U,S}
But we must toss out any duplicate items. After doing so we have
P = {P, R, E, O, S, T, U}
which in alphabetical order would be
P = {E, O, P, R, S, T, U}
There are n = 7 unique letters in this set.
So there are 2^n = 2^7 = 128 subsets and (2^n)-1 = (2^7)-1 = 128-1 = 127 proper subsets.
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note: If B is a subset of A, then everything inside B is also inside A. But not necessarily the other way around. A proper subset is one where set B is smaller than set A (it has at least one fewer items).
