Using properties of sets, show that A ∪ (A ∩ B) = A

Using properties of sets, show that:

(i) A ∪ (A ∩ B) = A

(ii) A ∩ (A ∪ B) = A.

Asked by Abhisek | 1 year ago | 119

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1 Answer

Solution :-

(i) To show: A ∪ (A ∩ B) = A

We know that,

A ⊂ A

A ∩ B ⊂ A

A ∪ (A ∩ B) ⊂ A .............(i)

Also, according to the question,

We have:

A⊂ A ∪ (A ∩ B)............... (ii)

Hence, from equation (i) and (ii)

We have:

A ∪ (A ∩ B) = A

(ii) To show,

A ∩ (A ∪ B) = A

A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B)

= A ∪ (A ∩ B)

= A

Answered by Pragya Singh | 1 year ago

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