 
Summary: HOMEWORK SOLUTIONS FOR MATH 5651
HOMEWORK FOR WEEK 1 OF FALL 2011
Text: de Groot and Schervish, 4th edition
Assignment: §1.4: 4,6,7; §1.5:4,5,6,8,9; §1.6: 2,3; §1.7: 3,5,7,8,9;
Problems 4 of §1.4
This problem is to prove Theorem 1.4.11. We will take the previous theorems
in the book, in particular Theorems 1.4.9 and 1.4.10, for granted. Let A and B be
any two sets. The first thing to prove is that A B and A Bc
are disjoint, i.e.,
that (A B) (A Bc
) = . Well,
(A B) (A Bc
) = A (B (A Bc
)) (Thm. 1.4.6)
= A ((A Bc
) B) (Thm. 1.4.4)
= A (A (Bc
B)) (Thm. 1.4.6)
= A (A (B Bc
)) (Thm. 1.4.4)
