For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
Students can take French or Sanskrit as their third language.

If $p, q, r$ are simple propositions with truth values $T, F, T$ respectively,then the truth value of $(\sim p \vee q) \wedge \sim r \Rightarrow p$ is

Check whether "Or" used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer.
$t:$ You are wet when it rains or you are in a river.

Find the component statements of the following compound statement and check whether they are true or false.
$100$ is divisible by $3, 11$ and $5$.

Consider the following three statements:
$P: 11$ is a prime number.
$Q: 7$ is a factor of $176$.
$R$: $LCM$ of $3$ and $7$ is $21$.
Then,the truth value of which one of the following statements is true?

The negation of the statement $p \rightarrow (q \wedge r)$ is equal to .........