Which of the following Boolean expressions is a tautology?

Negation of the statement "The payment will be made if and only if the work is finished in time." is

Which of the following statement patterns is a tautology?
$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$
$S_{2} \equiv \sim p \vee \sim q$
$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$
$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$

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 $3x^{2} - x - 10 = 0$.

For integers $m$ and $n$,both greater than $1$,consider the following three statements:
$P$: $m$ divides $n$
$Q$: $m$ divides $n^2$
$R$: $m$ is prime
Which of the following statements is true?

The negation of the statement "For all real numbers $x$ and $y, x+y=y+x$" is