State whether the "Or" used in the following statement is "exclusive" or "inclusive". Give reasons for your answer.
All integers are positive or negative.

Find the component statements of the following and check whether they are true or not.
Chandigarh is the capital of Haryana and $UP$.

The logical statement $[\sim(\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to

If $p$ and $q$ each have truth value $F$,then the truth values of the statement patterns $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$ and $\sim p \leftrightarrow (p \rightarrow \sim q)$ respectively are

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:

If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow [\sim r \wedge q]$ is False,then which of the following has truth value False?