$${p \Rightarrow q}$$  is false only when $$p$$ is true and $$q$$ is false.
$${\therefore p \Rightarrow q}$$   is false when $$p$$ is true and $${p \vee r}$$  is false, and $${q \vee r}$$  is false when both $$q$$ and $$r$$ are false.

Let $$p :$$ Paris is in France, $$q :$$ London is in England
$$\therefore $$ we have $${p \wedge q}$$
Its negation is $$ \sim \left( {p \wedge q} \right) = \,\, \sim p \vee \sim q$$
i.e., Paris is not in France or London is not in England.