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0 votes
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in Mathematics by (2.5k points)

Using properties of sets show that 

(i) A ∪ (A ∩ B) = A 

(ii) A ∩ (A ∪ B) = A. 

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1 Answer

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by (2.5k points)

(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 

(ii)To show: 

A ∩ (A ∪ B) = A

 A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B) 

= A ∪ (A ∩ B)  9 = A 

{from (1)} 

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