Question

If A and B are sets and AUB=AnB,then:
a. A={ }
b. B={ }
c. A=B
d. none of these​

Answer 1

c. A=B

as the intersection{common part} and union{addition of both the parts} are equal

I'll quote proof it must HELP

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

MARK BRAINLIEST

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If A and B are sets and A ∪ B = A ∩ B then

a. A = { }

b. B = { }

c. A = B

d. None of these

EVALUATION

Here it is given that A and B are sets and A ∪ B = A ∩ B

Now we show that A ∪ B = A ∩ B implies A = B

Let x ∈ A

⇒ x ∈ A ∪ B

⇒ x ∈ A ∩ B

⇒ x ∈ B

∴ A ⊆ B - - - - - (1)

Next let x ∈ B

⇒ x ∈ A ∪ B

⇒ x ∈ A ∩ B

⇒ x ∈ A

∴ B ⊆ A - - - - - (2)

From Equation 1 and Equation 2 we get

A = B

FINAL ANSWER

Hence the correct option is c. A = B

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