Consider the following two propositions :
$$P_1 : \sim p \to \sim q$$
$$P_2 : p \wedge \sim q \wedge \sim p \vee q$$
If the proposition $$p \to \sim p \vee q$$ is evaluated as FALSE, then

A

$$P_1$$ is TRUE and $$P_2$$ is FALSE

B

$$P_1$$ is FALSE and $$P_2$$ is TRUE

C

Both $$P_1$$ and $$P_2$$ are FALSE

D

Both $$P_1$$ and $$P_2$$ are TRUE