1. The problem statement, all variables and given/known data Can anyone please help me solve these questions? (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. Thank you for your time. 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???