9. For a finite set A, let N(A) denote the number of elements in A.

(a) Show that N(A U B) = N(A) + N(B) - N(AB)

(b) More generally, show that N

(

∪

i=1 A

i

)

= ΣN(A i

) - ΣΣN(A i

A j

) + ... + (-1)

n+1 P(A 1

, ..., A n

)