If $p$ and $q$ are simple propositions,then $p \Rightarrow q$ is false when

$p \Rightarrow q$ can also be written as

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

If $p: \forall n \in N, n^2+n$ is an even number and $q: \forall n \in N, n^2-n$ is an odd number,then the truth values of $p \wedge q, p \vee q$ and $p \rightarrow q$ are respectively:

The dual of the statement pattern $\sim p \wedge (q \vee t)$ is (where $t$ is a tautology and $c$ is a contradiction).

Consider the following statements:
$r: \text{If } p \to q \text{ is false, then } p \vee q \text{ is false.}$
$s: \text{If } p \leftrightarrow q \text{ is false, then } p \vee q \text{ is false.}$
The truth values of $r \to s$ and $s \to r$ are respectively: