# Set Proof Problems

1. Oct 15, 2016

### Ayushi160695

1. The problem statement, all variables and given/known data

(1) Prove that (A-B) - (B-C) = A-B

(2)Simplify (A-( A N B)) N (B-(ANB))

(3) Simplify ( ( A N ( B U C)) N ( A-B)) N ( B U C')

(4)Use element property and algebraic argument to derive the property

(A-B) U (B-C) = (A U B) - (B N C)

(5) Derive the set identity A U (A NB) = A

(6) Derive the set identity A N ( A U B) = A

N stands for intersection.

2. Relevant equations
A-B = A N B'- Set Difference rules
A N ( A U B) - Distributive rule : (A N A) U (A N B)
(A' N B') = (A U B)' - De Morgans Law

3. The attempt at a solution
Distributive
rules A N (A U B) = ( A N A) U ( A N B) = A U (A NB) then I dont know how to go there, if i continue with associative rule I simply revert back to the initial step? Same for question 5. For Q 1 (A N B') N ( B' N C) and then I don't know how to go from there.
Q 2 and 3 got me confused with all the brackets to be honest...I don't even know which rules to use? Any hint???

Last edited: Oct 15, 2016
2. Oct 15, 2016

### PeroK

Have you ever seen the following definition that two sets are equal:

Sets $A$ and $B$ are equal if $x \in A \iff \ x \in B$

3. Oct 15, 2016

### Ayushi160695

I actually managed to get the answer to Q 5 and 6
Q 5 First we state that for all subset of B of the universal set, U U B = U and then we intersect both sides by A.
Q 6 We state that for all subset if B of the universal set, Null set = Null Set intersect B and then take union of both sides with A.
It was quite easy, I was quite dumb for not noticing before and now for the other questions...