Truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$. Then the truth values of $(\sim p…
Truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$. Then the truth values of $(\sim p \vee q) \rightarrow(p \vee \sim q)$ and $(p \wedge \sim q) \rightarrow(\sim p \wedge q)$ are respectively
$\mathrm{T}, \mathrm{F}$
$\mathrm{F}, \mathrm{T}$
$\mathrm{T}, \mathrm{T}$
$\mathrm{F}, \mathrm{F}$
Solution
Truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$
$\begin{aligned}
\therefore \quad & p \equiv T, q \equiv F, r \equiv F \\
& (\sim p \vee q) \rightarrow(p \vee \sim q) \\
& \equiv(\sim T \vee F) \rightarrow(T \vee \sim F) \\
& \equiv(F \vee F) \rightarrow(T \vee T) \\
& \equiv F \rightarrow T \\
& \equiv T \\
& (p \wedge \sim q) \rightarrow(\sim p \wedge q) \\
& \equiv(T \wedge \sim F) \rightarrow(\sim T \wedge F) \\
& \equiv(T \wedge T) \rightarrow(F \wedge F) \\
& \equiv T \rightarrow F \\
& \equiv F
\end{aligned}$