Show that A union B=A intersection …
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Gaurav Seth 6 years, 6 months ago
Let A = B
AUB = A
A intersection B = A implies A U B = A intersection B
A = B implies AU B = intersection B ---- (1)
Now 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 to B
= x belongs to B
so A subset of B --- (2)
Now we will let y belong to B which implies y belongs to A U B
= y belongs to A intersection B
= y belongs to A and y belongs to B
= y belongs to A
Therefore, B subset of A --- (3)
from (2) and (3) we get A=B
so 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
1Thank You