Question

For A = {1,2,3,4,5,6,7} determine the number
of:

(a) subsets of A

(b) nonempty subsets of A

(c) proper subsets of A

(d) nonempty proper subsets of A

Answer 1

For part (a) I get 128 using combinations (you can also use pascal's triangle): C(7,0) + C(7,1) +...+C(7,7) = 128
For (b) the number of non empty subsets is just the "number of subsets (including the empty subset)- 1" which is just 127.
For (c) I use combinations again getting C(7,6) = 7

Answer 2

For (d) I'm not sure if it would be 7 also or 6. I'm a bit confused as to whether or not an empty subset is considered a proper subset.