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(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

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

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(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

If $p, q$ and $r$ are three propositions,then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge ((\sim p) \vee r)\} \rightarrow ((\sim q) \vee r)$ false?

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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?