### 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?