I'm translating this question from French to English, and my French isn't that good so sorry if i make any mistakes.
Question is :
We provide the power set $P(\mathbb R)$ with a relation $R$ defined by $ARB$ if $A\subset B$. Show that $R$ is an Order Relation, and is it total?
Now I know that an order relation has to be: Reflexive, anti-symmetric and transitive.
But unfortunately I don't really understand what those mean either. I have a general idea but nothing concrete.
I know that since $\mathbb R\subset P(\mathbb R)$, then $P(\mathbb R)>\mathbb R$(?) and then?
I'm going to start my first college year in a month or so, so sorry if I made any mathematical horrendous errors.
If anyone can take some time from his and explain it with some better examples, I'd be truly grateful, thanks!