The statement pattern $p \wedge (q \vee \sim p)$ is equivalent to

Which of the following is a contradiction?

The negation of $(p \wedge q) \rightarrow (\sim p \vee r)$ is

Write the negation of the following statement:
Chennai is the capital of Tamil Nadu.

Write the following statement in the form "if $p$,then $q$":
$r$: You can access the website only if you pay a subscription fee.

Check whether the following statement is true or false by proving its contrapositive: If $x, y \in \mathbb{Z}$ such that $xy$ is odd,then both $x$ and $y$ are odd.