The Boolean expression $((p \wedge q) \vee (p \vee \sim q)) \wedge (\sim p \wedge \sim q)$ is equivalent to

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.

The converse of $[p \wedge (\sim q)] \rightarrow r$ is

Given the statement: "If you live in Delhi,then you have winter clothes."
Identify the following statements as contrapositive or converse of the given statement:
$(i)$ If you do not have winter clothes,then you do not live in Delhi.
$(ii)$ If you have winter clothes,then you live in Delhi.

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

The statements $p, q$ and $r$ have truth values True, False and False respectively. The truth values of a logical statement $[\sim (p \land \sim q) \lor (q \lor \sim r)]$ and its dual are, respectively.....