Let A 8 1 2 3 4 5 7 8 a How many subsets of A are there In

Let A = [8] = {1, 2, 3, 4, 5, 7, 8}.

(a) How many subsets of A are there? In other words, compute |P(A)|.

(b) How many subsets of A contain both 1 and 2?

(c) How many subsets of A have an odd number of elements?

(d) How many subsets of A have an even number of elements? (Note that has an even number of elements, namely zero.)

Solution

a) subsets of A = 7!

b) total number of subsets = 2⁷

odd number of subsets are = {1,3,5,7}= 2⁴

c) subsets of A have an odd number of elements = 2⁷- 2⁴

d) subsets which has even number = {2,4,8} = 2⁷ - 2³