GRE 9367 #60
Posted: Fri Oct 02, 2009 12:46 pm
Let A and B be subsets of M and let S(0)={A,B}. for i>= 0 define S(i+1) inductively to be the collection of subsets X of M that are of the form CUD , C inter D , M-C, where C, D are in S(i). let S be the union of all the S(i). What is the largest number of elements of S(i)?
A)4 B)8 C) 15 D)16 E)infinity
I tryed to solve this question by counting the sets and I always get 14 elements :
A,
B,
empty set,
M-A,
M-B,
M,
AUB,
A inter B,
AU(M-B),
Aint(M-B),
(M-A)UB,
(M-A)interB,
(M-A)U(M-B),
(M-A)inter(M-B)
The right answer happened to be D. What are the remaining uncounted set?
A)4 B)8 C) 15 D)16 E)infinity
I tryed to solve this question by counting the sets and I always get 14 elements :
A,
B,
empty set,
M-A,
M-B,
M,
AUB,
A inter B,
AU(M-B),
Aint(M-B),
(M-A)UB,
(M-A)interB,
(M-A)U(M-B),
(M-A)inter(M-B)
The right answer happened to be D. What are the remaining uncounted set?