Question

Can someone help with this one???

For the set P = p is a letter in "PREPOSTEROUS" there could be (BLANK) subsets and (BLANK) proper subsets.

Answer 1

Answers:

128 subsets

127 proper subsets

=======================================================

Step-by-step 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.

---------------------

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).