If p: The total prime numbers between 2 to 10 | vedclass

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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.

Vedclass · Answer

(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?

Similar Questions

By giving a counterexample,show that the following statement is false: "If $n$ is an odd integer,then $n$ is prime."

Consider the following statements:
$(A)$ If $3+3=7$,then $4+3=8$.
$(B)$ If $5+3=8$,then the earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true,then $5+6=17$.
Which of the following statements is correct?

The conditional $(p \wedge q) \Rightarrow p$ is :-

If truth values of statements $p, q$ are true,and $r, s$ are false,then the truth values of the following statement patterns are respectively:
$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$
$b: (\sim q \wedge \sim r) \leftrightarrow(p \vee s)$
$c: (\sim p \vee q) \rightarrow(r \wedge \sim s)$

Which of the following sentences are statements? Give reasons for your answer.
$Today$ is a windy day.

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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?