(chapter 6. http://fit.ir/en/download/ebooksclub.org__Discrete_Mathematics_with_Applications.pdf - 4th Ed. Exercise 7 on page 372 of the textbook...

(chapter 6.3) : http://fit.ac.ir/en/download/ebooksclub.org__Discrete_Mathematics_with_Applications.pdf - 4th Ed.

Exercise 7 on page 372 of the textbook (chapter 6.3). 

Question:  

Prove each statement that is true and find a

counterexample for each statement that is false. Assume all sets

are subsets of a universal set U.

For all sets A, B, and C, 

(A − B) ∩ (C − B) = A − (B ∪ C).

Question: Also, find sets A, B, C such that one of the following two sets is a proper subset of the other: Ac ∩ (B ∩ C)c and B△C.