Question

Prove that for any set A,B and C : (A-B) - (B-C) =A-B​

Answer 1

Step-by-step explanation:

( A - B ) - ( B - C ) = A - B

= A - B - B + C = A - B

SO, -B + C = A - B - A +B = 0

HENCE, B + C = 0

THEREFORE:

( A - B ) - ( B - C) = A - B - B + C = A - B - 0 = A - B

LHS = RHS

HENCE PROVED

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Answer 2

Given ,

A, B andC are any set.

To prove

(A-B) - (B-C) =A-B

Proof

(A-B) - (B-C) =A-B

A-B-B+C =A-B

So, - B+C=A-B-A+B=0

Hence, B+C=0

Therefore (A-B) - (B-C) =A-B

A-B- B+C =A-B-0

A-B- B+C =A-B

LHS=RHS

Hence proved