Prove or disprove: A - (B intersection C) = (A - B) union (A - C). while proving this i have used the case of an empty set. could you please tell if its okay to use empty set. i have to explain this in class why i have used empty set.

if A - (B intersection C) = then we can say by result hold by property we can say A - (B C)

solution:

First prove that A - (B C) is a subset of (A - B) (A - C)

means: A - (B C) (A - B) (A - C)

if A - (B intersection C) = then we can say by result hold by property we can say A - (B C)

let x A - (B intersection C)

then x A and x(B C) which implies that xB ORxC

if xB then x A-B which means x (A-B) (A - C)

if xC then x A - C which means x (A-B) (A - C)

both the points prove the same conclusion which is x (A-B) (A - C)

hence conclude A - (B C) (A - B) (A - C)

Now Prove A - (B C) is a superset of (A - B) (A - C)

means: A - (B C) (A - B) (A - C)

if (A - B) (A - C) = then we can say by result hold by property of we can say(A - B) (A - C)

let x (A - B) (A - C).

then x A-B which implies that xA ANDxB if xB which means xB C

hence x A- (B C)

then x A-C which means x A AND xC if xC which means xB C

hence x A- (B C)

both the

prove the same conclusion which is x A- (B C)

hence conclude: A - (B C) (A - B) (A - C)

By Q.E.D we can prove A - (B C) = (A - B) (A - C).