Question

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

Answer 1

HELLO DEAR,

QUESTION:-If A and B are two sets then A-B =B-A if,.............?

SOLUTION:- A and B are two sets

and A - B = B - A ,

if A = B.

Therefore ,we can say that the each element of set A belong to the every element of set B.

i) Difference of sets :- If A and B be two given sets ,then the set of all

those elements of A which do not belong to B is

called difference of sets A and B.It is written as A - B.

I HOPE IT'S HELP YOU DEAR,

THANKS.

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

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

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

So A - B = B - A

Next suppose that A - B = B - A

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

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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