Math, asked by Anonymous, 8 months ago

prove that AUB=A intersection B<=>A=B​

Answers

Answered by ankitgupta82
5
Answer ❎❎❎




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


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


=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




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Answered by Anonymous
8
Answer ❎❎❎




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


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


=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




Mark as Brainlist ✔✔✔❎❎
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