Question

Prove that \P(A) \cup \P(B) \subseteq \P(A \cup B) and find a counter-example to show that we don't always have equality

Answer 1

P(A) ∪ P(B) ⊆ P(A ∪ B) can be proved when
`X` ∈ P ( A U B )

Explanation:

To Prove that P(A) ∪ P(B) ⊆ P(A ∪ B) is attached below and also a counter example to prove that we do not always get an equality is attached below as well