Question

(A union B) = A intersection B proove​

Answer 1

$\huge \mathbf{answer}$

First let A=B . Then,

A U B=A and A intersection B= A implies A U B =A INTERSECTION B

Thus,   A=B implies AU B= A INTERSECTION B. .....(1)

Conversely, let A U B=A intersection

B.Then we have to prove that A=B. For this let x belongs to A implies x belongs to A U B

                                         =x belongs to A intersection B

                                         =x belongs to A and x belongs toB

                                         =x  belongs to B

therefore, A subset of B.    ......(2)

Now let,

y belongs to B implies y belongs to A U B

                                        =y belongs to A intersection B

                                        =y belongs to A and y belongs toB

                                       =y belongs to A

Therefore,       B subset of A.     .......(3)

From (2) and(3) , we get A=B.

Thus,   A U B = A intersection B implies A = B     .......(4)

From (1) and (4) , we obtain

            A U B = A INTERSECTION B  IMPLIES A = B