Prove that (A-B) intersection (A-C)= A-(B union C)?

[rainalebel]

Somebody please help me solve this..... Thank you..

 

[daon2]

what have you tried? Lets see what you can do, try proving one is the subset of the other first.

 

[SAMUELK]

Somebody please help me solve this..... Thank you..

SUGGESTION: Make a Venn Diagram -- the old 'three-ring sign' -- and number each of the eight regions, 1 - 8.

Now compute the region-set for the left- and right-sides of your equation and see if they match.

 

[pka]

SUGGESTION: Make a Venn Diagram -- the old 'three-ring sign' -- and number each of the eight regions, 1 - 8.

Why not use the rules?
Recall that \(\displaystyle A\setminus B=A\cap B^c\) and \(\displaystyle (B^c\cap C^c)=(B\cup C)^c.
\)
Rewrite and factor.