I think statement 1 is true

P(A) contains subsets of A, not the actual elements of A. So unless the elements of A themselves are sets, they won’t be inside P(A).

Example:

Let A = {1, 2}

Then P(A) = {∅, {1}, {2}, {1,2}}

Here, 1 and 2 are not elements of P(A), so A is not contained in P(A). Therefore,

A ∪ P(A) is not equal to P(A)

So statement I is false.

No it is not

A does not belong to P(A).

{A} belongs to P(A)