For any sets A and B, use algebraic laws of sets to simplify

(a) [ A - (A-B)] - B

(b) A - [ B - (A-B)]

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- Oct 22nd 2012, 04:49 AMmous99Algebraic laws to simplify
For any sets A and B, use algebraic laws of sets to simplify

(a) [ A - (A-B)] - B

(b) A - [ B - (A-B)] - Oct 22nd 2012, 05:04 AMBingkRe: Algebraic laws to simplify
Use $\displaystyle X \setminus Y = X \cap Y^c$ to convert the set minus into intersection/union of sets

- Oct 22nd 2012, 05:16 AMmous99Re: Algebraic laws to simplify
- Oct 22nd 2012, 05:42 AMBingkRe: Algebraic laws to simplify
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")