Show that A union B=A intersection B impliesA=B

1.	Show that A union B=A intersection B impliesA=B
Answer» Let A = BAUB = A\xa0A intersection B = A implies A U B = A intersection BA = B implies AU B = intersection B ---- (1)Now let A U B = A intersection\xa0B. 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 to B= x belongs to Bso A subset of B --- (2)Now we will let y belong to B which implies y belongs to A U B\xa0= y belongs to A intersection B= y belongs to A and y belongs to B= y belongs to ATherefore, B subset of A --- (3)from (2) and (3) we get A=Bso A union B will be equal to A intersection B implies A = B ---(4)From (1) and (4) we will get A union B = A INTERSECTION B Implies A = B

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