Question

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

A⊂B

B⊂A

A=B

None Of These​

Answer 1

Answer:

A=B is your answer..........

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

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

• A ⊂ B

• B ⊂ A

• A = B

• None Of These

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$\sf{A - B = \Phi}$

$\sf{B - A = \Phi}$

So A - B = B - A

Next suppose that A - B = B - A

If possible let A - B = B - A , a non empty set

$\sf{Let \: \: x \in \: A - B = B - A}$

Now $\sf{x \in \: A - B \: \: implies \: \: x \in A}$

$\sf{x \in \:B - A \: \: implies \: \: x \notin A}$

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

Hence A - B = B - A

Now $\sf{A - B = \Phi} \: \: implies \: \: A \subset \: B$

$\sf{B - A = \Phi} \: \: implies \: \: B \subset \: A$

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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