Symmetric Closure

[thesevensparks]

I can't seem to find the way to approach this problem. Because it has symbols I don't know how to type here, I have attached an image here instead. Please help me if you can. Any input would be greatly appreciated. Thank you.

[stapel_eliz]

I can't seem to find the way to approach this problem. Because it has symbols I don't know how to type here, I have attached an image here instead.

To learn how to format math as text, try here. To learn how to use some LaTeX formatting, try this post. LaTeX produces this:

Note: The above reads like a definition rather than a theorem ("this is defined as being that"). Are you supposed to be proving that the symmetric closure can be stated in this manner? If so, what definition and other information are you provided regarding symmetric closures?

Thank you!