Set Theory Proof: A vs. B-C vs. C

[courtrigrad]

Hi all

(i) A- (B-C) = (A-B) U C
(ii) A - (B U C) = (A-B) - C

Which one is always right and which is sometimes wrong?

My solution

If x is an element of A - (B-C), then x is not contained in B-C. If y is an element of (A-B) U C, then y is at least one of A-B or C. (i) is sometimes wrong, because y can be C.

If x is an element of A - (B U C), then x is not contained in (B U C). If y is an element of (A - B) - C, then y is not in B or C. Hence this is always correct. IS my solution correct? Also how would you make (i) true always?

Thanks

 

[TenaliRaman]

Coutrigrad,
Bravo!
You are correct and also the way u have done it is perfect!

-- AI

 

[courtrigrad]

thanks a lot!

 

[scan]

why not use venn diagram to check?

 

[TenaliRaman]

Scan,
who said not to?

-- AI