The entries in the last column of the truth table for $\sim(p \wedge q)$ are

If $p, q, r$ are simple propositions with truth values $T, F, T$ respectively, then which of the following is not a true statement?

The compound statement $(\sim(P \wedge Q)) \vee ((\sim P) \wedge Q) \Rightarrow ((\sim P) \wedge (\sim Q))$ is equivalent to

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.

Using the words "necessary and sufficient",rewrite the statement "The integer $n$ is odd if and only if $n^{2}$ is odd". Also,check whether the statement is true.

For each of the following compound statements,first identify the connecting words and then break it into component statements.
$x=2$ and $x=3$ are the roots of the equation $3x^{2} - x - 10 = 0$.