Given that A union B = C and A intersecting B = null set,
Prove :- C -B =A

Question

Rajat Sethi · Accepted Answer

Given,A∩B=∅⇒A∩B'=A
(i)Now,A∪B=CTaking intersection with B' on both sides,(A∪B)∩B'=C∩B'⇒(A∩B')∪(B∩B')=C∩B'⇒A∪∅=C∩B' 
[From (i)]⇒C∩B'=A (ii)Now,C-B=C∩B'=A
[From (ii)]

Given that A union B = C and A intersecting B = null set, Prove :- C -B =A

Given that A union B = C and A intersecting B = null set,
Prove :- C -B =A