Question

Why $(p\wedge q)\Rightarrow r$ is true when p is true and q is false.

Answer 1

if we have predicate $p$ and $q$ the $p\Rightarrow q$ is true when either $p$ is false or $q$ is true.

(or both) that is

$\left(p\Rightarrow q\right)\iff \left(-p\vee q\right)$

The implication will not hold only when $p$ is true and $q$ is false.

That is $p\vee -q$ is true.

So in question, $p$ is true and $q$ is false

So, $p\vee q$ is false. Thus $p\vee q\Rightarrow r$ is indeed true.

$\left(\left(p\vee q\right)\Rightarrow r\right)\iff \left(-p\left(p\vee q\right)\vee r\right)$.