Question

Solve for 50 points guys....
.
.
.
.
.
..
.
Show that A union B = A intersection B implies A=B

Answer 1

Answer:

Step-by-step explanation:

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