Question 8 (1 point)

Let S = {1, 2, 3,... n} where n is

even. What is the relationship between the

number of subsets S of with odd cardinality,

and the number of subsets of S with even

cardinality.

Explain your answer.

Hint: Each subset either contains the

element 1 or it doesn't. Consider all the

subsets that do not contain the element 1.

Some of these have odd cardinality and

some have even cardinality. What happens

when you include the element 1 in each of

these subsets?