Prove A-(B-C) = (A-B) U (A intersect C) for any sets A,B and C.

How do we prove it without using the Venn diagram?

Question

Prove A-(B-C) = (A-B) U (A intersect C) for any sets A,B and C

How do we prove it without using the Venn diagram?

Varun.Rawat · Accepted Answer

LHS = A - B-C=A - B∩C'=A∩B∩C''=A∩B'∪A∩C=A-B∪A∩C=RHS