The negation of inverse of $~p\to q$ is ______.

Which of the following sentences are statements in logic? Justify. Write down the truth value of the statements:

$4!=24$

Which of the following sentences are statements in logic? Justify. Write down the truth value of the statements:

$\pi$ is an irrational number.

Which of the following sentences are statements in logic? Justify. Write down the truth value of the statements:

India is a country and Himalayas is a river.

Which of the following sentences are statements in logic? Justify. Write down the truth value of the statements:

Please get me a glass of water.

Which of the following sentences are statements in logic? Justify. Write down the truth value of the statements:

${\cos }^2\theta -{\sin }^2\theta =\cos 2\theta \text{for all }\theta \in R.$

State which of the following are statements. Justify. In case of statement, state its truth value.

If $x$ is a whole number then $x+6=0$