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

Solution:

(i) A υ (A ∩ B) = A

We know that

A ⊂ A

A ∩ B ⊂ A

A υ (A ∩ B) ⊂ A ....(1)

Also,

A ⊂ A υ (A ∩ B) ....(2)

From (1) and (2),

A υ (A ∩ B) = A

(ii) A ∩ (A υ B) = A

A ∩ (A υ B) = (A ∩ A) υ (A ∩ B)

= A υ (A ∩ B)

A ∩ (A υ B) = A [from (1)]

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NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 9

Using properties of sets show that (i) A υ (A ∩ B) = A (ii) A ∩ (A υ B) = A

Two sets are given. We have proved that A ∩ (A υ B) = (A ∩ A) υ (A ∩ B)