If $p$: It rains today,$q$: $I$ go to school,$r$: $I$ shall meet my friend,and $s$: $I$ shall go for a movie,then which of the following represents the proposition: "If it does not rain or if $I$ do not go to school,then $I$ shall meet my friend and go for a movie"?
- A$\sim (p \wedge q) \Rightarrow (r \wedge s)$
- B$\sim (p \wedge \sim q) \Rightarrow (r \wedge s)$
- C$\sim (p \wedge q) \Rightarrow (r \vee s)$
- DNone of these
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The negation of the inverse of $\sim p \rightarrow q$ is
If the truth value of the expression $[(p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r)]$ $\rightarrow (p \wedge q)$ is False,then the truth values of $p, q, r$ are respectively:
If $p$: Every square is a rectangle and $q$: Every rhombus is a kite,then the truth values of $p \rightarrow q$ and $p \leftrightarrow q$ are $ . . . . . . $ and $ . . . . . . $ respectively.
Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is
Which of the following statement patterns is a tautology?
$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
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$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
$S_4 \equiv (p \wedge q) \rightarrow r$
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