Ordinal Problem.

Hi, the question posed to me is as follows:

Prove or find a counterexample to:

1. is an ordinal is an ordinal
2. is an ordinal is an ordinal

I've found proofs to both of these questions but I'm not entirely sure that they are both correct. Can anyone see a way these implications do not hold?

Thank you.

a u {a} is an ordinal <-> a is an ordinal.

a is an ordinal -> a u Ua is an ordinal.

But it it does not hold for all a that

a u Ua is an ordinal -> a is an ordinal.

You should find a simple example of an a such that a u Ua is an ordinal but a is not an ordinal.