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

The statement $[(p$ $\rightarrow q) \wedge \sim q]$ $\rightarrow r$ is a tautology,when $r$ is equivalent to

Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $(p \nabla q) \Rightarrow ((p \nabla q) \nabla r)$ is a tautology. Then $(p \nabla q) \Delta r$ is logically equivalent to

The negation of the converse of the statement $p \lor q$ is:

Negation of the Boolean expression $p \Leftrightarrow (q \Rightarrow p)$ is:

By giving a counterexample,show that the following statement is not true.
$q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.