If ${(p \wedge \sim q) \wedge (p \wedge r)} \rightarrow (\sim p \vee q)$ has a truth value of $False$,then the truth values of the statements $p, q, r$ are respectively:

The statements $p, q$ and $r$ have truth values True, False and False respectively. The truth values of a logical statement $[\sim (p \land \sim q) \lor (q \lor \sim r)]$ and its dual are, respectively.....

Consider the three statements -
$p: \forall n \in N, 10n-3$ is a prime number,when $n$ is not divisible by $3$.
$q: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.
$r: \sin x$ is an increasing function in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$.
Then which of the following statement patterns has a truth value of true?

What is the statement $(p \wedge q) \rightarrow p$?

By giving a counterexample,show that the following statement is false: "If $n$ is an odd integer,then $n$ is prime."

For each of the following compound statements,first identify the connecting words and then break it into component statements.
Square of an integer is positive or negative.