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(C) First,determine the truth values of the statements:$p$: The prime numbers between $2$ and $100$ are $25$,not $26$. So,$p$ is $F$.$q$: Zero $(0)$ c

Vedclass · Accepted Answer

$(p \vee q) \leftrightarrow r$ has truth value False.

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(C) First,determine the truth values of the statements:$p$: The prime numbers between $2$ and $100$ are $25$,not $26$. So,$p$ is $F$.$q$: Zero $(0)$ can be written as $0 + 0i$,which is a complex number. So,$q$ is $T$.$r$: The $L$.$C$.$M$. of $6$ and $7$ is $42$,not $6$. So,$r$ is $F$.Now evaluate the options:$(A)$ $(p \wedge q)$ $\rightarrow r \equiv (F \wedge T)$ $\rightarrow F \equiv F$ $\rightarrow F \equiv T$.$(B)$ $(p$ $\rightarrow q)$ $\rightarrow r \equiv (F$ $\rightarrow T)$ $\rightarrow F \equiv T$ $\rightarrow F \equiv F$.$(C)$ $(p \vee q) \leftrightarrow r \equiv (F \vee T) \leftrightarrow F \equiv T \leftrightarrow F \equiv F$.$(D)$ $(p$ $\rightarrow q)$ $\rightarrow (q$ $\rightarrow p) \equiv (F$ $\rightarrow T)$ $\rightarrow (T$ $\rightarrow F) \equiv T$ $\rightarrow F \equiv F$.Thus,option $(C)$ is correct.

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?

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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?