Question

Using properties of sets show that (i) $A ∪ (A ∩ B) = A$** (ii)** $A ∩ (A ∪ B) = A.$

Answer 1

(i) To show: $A ∪ (A ∩ B) = A$
We know that
$A ⊂ A$
$A ∩ B ⊂ A$
$∴ A ∪ (A ∩ B) ⊂ A … (1)$
Also, $A ⊂ A ∪ (A ∩ B) … (2)$
∴ From (1) and (2) ,$A ∪ (A ∩ B) = A$

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(ii) To show: $A ∩ (A ∪ B) = A$
$A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B)$
$= A ∪ (A ∩ B)$
$= A$ {from (1)}