Question 765392
Set A= {1,3,2,5}
 Set B= {2,4,6}
 Set C= {1,3,5}

AUBUC = {1,2,3,4,5,6} - 6 elements

How many subsets does this have?
No. of 1-element subsets = C(6,1) = 6
No. of 2-element subsets = C(6,2) = 6*5/(1*2) = 15
No. of 3-element subsets = C(6,3) = (6*5*4)/(1*2*3) = 20
No. of 4-element subsets = C(6,4) = C(6,2) = 15
No. of 5-element subsets = C(6,5) = C(6,1) = 6
No. of 6-element subsets = C(6,6) = 1
Null subset {} = 1

So the total number of subsets = 64
(In general, number of subsets of a set with n elements = 2^n)

b) which set is not a subset of A U(union) C?

AUC = {1,2,3,5}

Clearly the answer is (D) i.e. {4} since 4 is not an element of AUC.

:)