Is the following a valid inference?

$($p $->$ q$)($p $->$ r$)|=($q $$ r$)$

Explain your answer. $[2]$

$($c$)$ Consider the binary relation R on the set of propositional sentences

defined by setting, for any sentences A$,$ B:

ARB iff A $|=$ B

Is R an equivalence relation? Justify your answer with the help of

your answer to part $($b$)$ above. You must clearly state in full any other

definitions or results from the lecture notes that you rely on in your

explanation.