Would someone mind checking my proof? Intro Real Analysis

[CaptainAmerica17]

Homework Statement

Show that if f: A -> B and E, F are subsets of A, then f(E U F)=f(E) U f(E).

Relevant Equations

Basic proof stuff.

Here is my solution. I used mathjax to type it up in Overleaf. I feel like it makes sense, but I also have a feeling I might have "jumped the gun" with my logic. If it is correct, I would appreciate feedback on how to improve it. Thanks!

 

[PeroK]

Looks good. The probem is a bit easy for a superhero, I would have said!

 

[CaptainAmerica17]

Looks good. The probem is a bit easy for a superhero, I would have said!

LOL! Thanks for checking XD