Question

If A U B = A intersection B then

Answer 1

Answer:

A=B

Step-by-step explanation:

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Show that A ∪ B = A ∩ B imp...

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Show that A∪B=A∩B implies A=B

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ANSWER

let x∈A then x∈A∪B

since , A∪B=A∩B

x∈A∩B

So, x∈B

i.e., if an element belongs to set A, then it must belong to set B also.

∴A⊂B.....(i)

Similarly, if y∈B then, y∈A∪B

Since A∪B=A∩B

y∈A∩B

So, y∈A

∴ if y∈B

then y∈A

A⊂A.....(ii)

from (i) and (ii)

A⊂B and B⊂A

thus A=B