Let A, B, C be three sets. If A U B= C and A intersection b = null set, prove that A= C-B

U = Union

^ = Intersection

B' = Bcompliment

.

A ^ B = Null

Therefore A ^ B' = A

.

AUB = C

(AUB) ^ B' = C ^ B' ......... (Intersection LHS and RHS with B compliment)

.

By distributive property,

(AUB) ^ B' = C ^ B'

(A^B') U (B^B') = C ^ B'

.

As proved before A ^ B' = A and also C ^ B' = C-B

.

Therefore,

(A^B') U (B^B') = C ^ B'

(A) U (nullset) = C-B

A = C - B.

.

Hence proved.