Need help

[rustic cedar]

Can anyone review my solution, any other thing i could do better:

[fluid tangle]

The only remarks I have are the following:

1. Equality is used (at least in mathematics) for equations, while for propositions and logical equivalences we use the symbol $\iff$ (if and only if)

[thin fossil]

bondalton

[fluid tangle]

2. The last line
   [\forall x\in A\cup B P(x)]
   Makes no mathematical sense. Recall that implication in this case (set theory) is mostly used to prove subset like relations, so the last line should read
   [A\cup B\subseteq{x\ :\ P(x)}]
   If it's not clear why, I'd recommend to read again the definition of the symbol $\subseteq$.

[thin fossil]

bondalton