Let A={9,10,11,12,13,15,16}

Question

How many subsets does A have

How many proper subsets a have

Answer 1

a set A with n elements has 2ⁿ subsets

A has 7 elements

there are 2⁷=2*2*2*2*2*2*2=128 subsets

a proper subset, B, of A, does not equal A; A has at least 1 element that B does not have

there are 127 proper subsets

you can also find the answer the long way...

the null or empty set=1 set

the set itself=1 set

the sets with 1 element=7 sets

the sets with 2 elements=7C2=21 sets

the sets with 3 elements=7C3=35 sets

4 elements=7C4=35 sets

5 elements=7C5=21 sets

6 elements=7C6=7 sets

add the numbers of sets to get 128 sets