If p: 25 is an odd prime number. q: 14 is a c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) First,we evaluate the truth values of the given statements: $p: 25$ is an odd prime number. Since $25 = 5 	imes 5$,it is a composite number. Thus

Vedclass · Accepted Answer

$\sim p \vee (q \wedge r)$

Vedclass · Answer

(D) First,we evaluate the truth values of the given statements: $p: 25$ is an odd prime number. Since $25 = 5 	imes 5$,it is a composite number. Thus,$p \equiv F$. $q: 14$ is a composite number. Since $14 = 2 	imes 7$,it is a composite number. Thus,$q \equiv T$. $r: 64$ is a perfect square number. Since $64 = 8^2$,it is a perfect square. Thus,$r \equiv T$. Now,we evaluate the options: $A: \sim(q \wedge r) \vee p \equiv \sim(T \wedge T) \vee F \equiv \sim T \vee F \equiv F \vee F \equiv F$. $B: (p \wedge q) \vee r \equiv (F \wedge T) \vee T \equiv F \vee T \equiv T$. $C: (p \vee q) \wedge (\sim r) \equiv (F \vee T) \wedge (\sim T) \equiv T \wedge F \equiv F$. $D: \sim p \vee (q \wedge r) \equiv \sim F \vee (T \wedge T) \equiv T \vee T \equiv T$. Note: Both $B$ and $D$ result in $T$. Based on the provided solution,$D$ is the intended answer.

If $p: 25$ is an odd prime number.
$q: 14$ is a composite number and
$r: 64$ is a perfect square number.
Then which of the following statement patterns is true?

Similar Questions

Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

The negation of the statement $(p \wedge q) \rightarrow (\sim p \vee r)$ is

If the truth value of the logical statement $(p \leftrightarrow \sim q) \rightarrow (\sim p \wedge q)$ is false,then the truth values of $p$ and $q$ are respectively:

Statement $-1$: The statement $A \to (B \to A)$ is equivalent to $A \to (A \vee B)$.
Statement $-2$: The statement $\sim [(A \wedge B) \to (\sim A \vee B)]$ is a tautology.

If $p \Rightarrow (\sim p \vee q)$ is false,the truth values of $p$ and $q$ are respectively

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If $p: 25$ is an odd prime number. $q: 14$ is a composite number and $r: 64$ is a perfect square number. Then which of the following statement patterns is true?