Simplifying a logic expression

Question

$p \Rightarrow q$ is true

Which is the logic value of $(p \vee r) \Rightarrow (q \vee r)$ ?

I did at this point and I can not siplify it more:

$\neg (p \vee r) \vee (q \vee r)$

$(\neg p \wedge \neg r) \vee ( q \vee r)$

Could someone help me please and explain how should I simplify it?

Answer 1

If truth value of $r$ is $T$, then $p\lor T\implies q\lor T\equiv (T\implies T)\equiv T$.

If truth value of $r$ is $F$, then $p\lor F\implies q\lor F\equiv (p\implies q)\equiv T$.