Algebraic laws to simplify

Oct 2012
32
0
malaysia
For any sets A and B, use algebraic laws of sets to simplify
(a) [ A - (A-B)] - B
(b) A - [ B - (A-B)]
 
Aug 2009
170
36
Use \(\displaystyle X \setminus Y = X \cap Y^c\) to convert the set minus into intersection/union of sets
 
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Oct 2012
32
0
malaysia
Use \(\displaystyle X \setminus Y = X \cap Y^c\) to convert the set minus into intersection/union of sets
How to put the set minus into the set?(Cool)
 
Aug 2009
170
36
I don't understand your question ...

Example:
\(\displaystyle X \setminus ( Y\setminus Z) = X \ ( Y \cap Z^c) = X \cap (Y \cap Z^c)^c = X \cap (Y^c \cup Z) = \\ (X \cap Y^c) \cup (X \cap Z)\)

The last line is from distribution (you can check Algebra of sets - Wikipedia, the free encyclopedia for more "shortcuts")