Let the set A be defined as follows.

Question

A={m,c,g,l,w,d}

(a) Find the total number of proper subsets of A	.
(b) Find the total number of subsets of A	.

Answer 1

A is an improper subset

for proper subsets subtract 1

6 elements of the set

the total subsets = 2^6 = 64

proper subets = 64-1 = 63

total subsets includes the set A itself

there is one improper subset with 6 elements, A

there are 6 subsets with 5 elements

10 subsets with 4 elements

15 with 3 elements

10 with 2 elements

6 with 1 element each

1 with 0 element, the null set

proper subsets includes any subset except A

add them to get 1+6+10+15+20+15+10+6+1 = 64

add the 7th row of Pascal's triangle