Write the following statement in the form "if $p$,then $q$":
$p$: It is necessary to have a password to log on to the server.

If $p$: It is raining and $q$: It is pleasant,then the symbolic form of "It is neither raining nor pleasant" is

If $c$ denotes the contradiction,then the dual of the compound statement $\sim p \wedge (q \vee c)$ is:

Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \geq 1$.

If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If a triangle $ABC$ is equilateral,then it is isosceles.