SOLUTION: Set A= {1,3,2,5} Set B= {2,4,6} Set C= {1,3,5} 9. How many subsets does A U(union)parenthesis B U(union) C close parenthesis have? A) 2 B) 4 C) 16 D) 32

Question 765392: Set A= {1,3,2,5}
Set B= {2,4,6}
Set C= {1,3,5}
9. How many subsets does A U(union)parenthesis B U(union) C close parenthesis have?
A) 2
B) 4
C) 16
D) 32
E) 64
10. which set is not a subset of A U(union) C?
A) { }
B) A
C) C
D) {4}
E) {1,2,5}
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
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.
:)
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