Which of the following statements is a contradiction?

Given the following two statements:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:

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

Check the validity of the statement given below by the method specified against it.
$p:$ The sum of an irrational number and a rational number is irrational (by contradiction method).

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

Write the negation of the following statement:
$\sqrt{7}$ is rational.