Discrete Math: Symmetric Closure & Numerical Analysis

[thesevenspark]

Discrete Mathematics -- Symmetric Closure Math help in Numerical Analysis, Systems of

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.

 

[issacnewton]

hi

let $$S=R \cup R^{-1}$$ , to prove that S is symmetric closure of R you have to prove
three things

$$1)\cdots R\subseteq S$$

$$2) \cdots S \;\mbox{is symmetric}\;$$

$$3)\cdots \forall T \subseteq A\times A [(R\subseteq T)\wedge(T\;\mbox{is symmetric}\;)\Rightarrow (S\subseteq T)]$$


can you prove 1 now ?