Question 1169634
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            (1)   First,  I will prove that every element  "x"  which belongs to set  A,  belongs to set  B,  too.


            (2)   Next,  I will prove that every element  "y"  which belongs to set  B,  belongs to set  A,  too.


                    It will mean that the sets  A  and  B  are identical.



<pre>
    Indeed, let x belongs to A.

    Then it belongs to (A union B).

    Due to condition, it implies that x belongs to (A intersection B).

    In turn, it means that x belongs to B.

    First statement is proved.
</pre>


Now I prove the second statement (the proof is the same due to symmetry)


<pre>
    Let y belongs to B.

    Then y belongs to (A union B).

    Due to condition, it implies that y belongs to (A intersection B).

    In turn, it means that y belongs to A.

    Second statement is proved.
</pre>

With two statements proven, &nbsp;the posed problem is solved.