For any two sets A and B, prove that (i) B ⊂ A ∪ B (ii) A ∩ B ⊂ A

Answers:

(i) 

Consider,

p ∈ B

p ∈ B ∪ A

∴ B ⊂ A ∪ B

(ii)

Consider,

p ∈ A ∩ B

p ∈ A and p ∈ B

∴  A ∩ B ⊂ A