Question -
Answer -
(i) B ⊂ A ∪ B
Let us consider an element ‘p’ such that it belongs to B
∴ p ∈ B
p ∈ B ∪ A
B ⊂ A ∪ B
(ii) A ∩ B ⊂ A
Let us consider an element ‘p’ such that it belongs to B
∴ p ∈ A ∩ B
p ∈ A and p ∈ B
A ∩ B ⊂ A
(iii) A ⊂ B ⇒ A ∩ B = A
Let us consider an element ‘p’ such that it belongs to A ⊂ B.
p ∈ A ⊂ B
Then, x ∈ B
Let and p ∈ A ∩ B
x ∈ A and x ∈ B
x ∈ A and x ∈ A (since, A ⊂ B)
∴ (A ∩ B) = A