For sets A, B and C using properties of sets , prove that 1. A-(B-C)=(A-B)union (A intersection C) 2.A intersection (B-C)=(A intersection B)-(A intersection C) Share with your friends Share 14 Lovina Kansal answered this Dear student We have,1) A-B-C=A-B∩C' ∵B-C=B∩C'=A∩(B∩C')' [∵X-Y=X∩Y']=A∩(B'∪C) [∵(B∩C')'=B'∪(C')'=B'∪C=(A∩B')∪(A∩C)=(A-B)∪(A∩C)2) A∩(B-C)= (A∩B)-(A∩C)Let x be any arbitary element of A∩(B-C).Then,⇒x∈A∩(B-C)⇒x∈A and x∈(B-C)⇒x∈A and (x∈B and x∉C)⇒(x∈A and x∈B) and (x∈A and x∉C)⇒x∈(A∩B) and x∉(A∩C)⇒x∈(A∩B)-(A∩C)∴A∩(B-C)⊆(A∩B)-(A∩C)Similarly,(A∩B)-(A∩C)⊆ A∩(B-C)Hence,A∩(B-C)= (A∩B)-(A∩C) Regards -9 View Full Answer