Question

if A and B are two sets then A-B=B-A if ?​

Answer 1

Answer:

If all elements in A is present in B, then you can say that A-B=B-A.

Answer 2

SOLUTION

TO DETERMINE

If A and B are two sets then A-B =B-A if

EVALUATION

First we prove that If A and B are two sets then A-B =B-A iff A = B

First suppose that A = B

Then

\sf{A - B = \Phi}A−B=Φ

\sf{B - A = \Phi}B−A=Φ

So A - B = B - A

Next suppose that A - B = B - A

\sf{Let \: \: x \in \: A - B = B - A}Letx∈A−B=B−A

Now

\sf{x \in \: A - B \: \: implies \: \: x \in A}x∈A−Bimpliesx∈A

\sf{x \in \:B - A \: \: implies \: \: x \notin A}x∈B−Aimpliesx∈

/

A

---------- a contradiction

Hence A - B = B - A

Now

\sf{A - B = \Phi} \: \: implies \: \: A \subset \: BA−B=ΦimpliesA⊂B

\sf{B - A = \Phi} \: \: implies \: \: B \subset \: AB−A=ΦimpliesB⊂A

Together gives A = B

FINAL ANSWER

If A and B are two sets then A-B =B-A

if A = B

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