Question

If A and B are two sets, simplify A∩(A∪B) .​

Answer 1

Answer:

Union means addition of all the elements of both the sets. Intersection means common elements of both the sets. It indicates B is a empty set or have same elements which set A have because at union fuction also the answer is A. ANB=A or ANB=B.

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Answer 2

Given:

A and B are two sets that have nothing in common.

To find:

Simplify the relation A∩(A∪B).

Solution:

The given equation is A∩(A∪B).

Now firstly lets expand the equation, on expanding we will get:

(A∩A) ∪ (A∩B)

Now A∩B will give nothing because A and B have nothing in common but A∩A = A

So the equation will be simplified as A∩(A∪B) = A + 0

Hence A∩(A∪B) = A

Therefore on simplifying the equation A∩(A∪B) we get A∩(A∪B) = A.