If p : The total prime numbers between 2 to 100 are 26 . q : Zero is a complex number. r : Least common…
If p : The total prime numbers between 2 to 100 are 26 .
q : Zero is a complex number.
r : Least common multiple (L.C.M.) of 6 and 7 is 6 .
Then which of the following is correct?
$(p \wedge q) \rightarrow r$ has truth value False.
$(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{r}$ has truth value True.
$(p \vee q) \leftrightarrow r$ has truth value False.
$(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow(\mathrm{q} \rightarrow \mathrm{p})$ has truth value True.
Solution
The truth values of $\mathrm{p}, \mathrm{q}$ and r are $\mathrm{F}, \mathrm{T}$ and F respectively.
Consider option (C)
$\begin{aligned}
& (p \vee q) \leftrightarrow r \\
& \equiv(F \vee T) \leftrightarrow F \\
& \equiv T \leftrightarrow F \\
& \equiv F .
\end{aligned}$