For integers m and n,both greater than 1,cons | vedclass

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(A) We evaluate the truth value of each implication by testing counterexamples:For option $(D)$,$Q 	o P$: Let $m = 8$ and $n = 4$. Here $n^2 = 16$. S

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$Q \wedge R 	o P$

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(A) We evaluate the truth value of each implication by testing counterexamples:For option $(D)$,$Q 	o P$: Let $m = 8$ and $n = 4$. Here $n^2 = 16$. Since $8$ divides $16$,$Q$ is true. However,$8$ does not divide $4$,so $P$ is false. Thus,$Q 	o P$ is false.For option $(C)$,$Q 	o R$: Let $m = 12$ and $n = 6$. Here $n^2 = 36$. Since $12$ divides $36$,$Q$ is true. However,$12$ is not prime,so $R$ is false. Thus,$Q 	o R$ is false.For option $(B)$,$P \wedge Q 	o R$: Let $m = 4$ and $n = 8$. $P$ is true ($4$ divides $8$) and $Q$ is true ($4$ divides $64$). However,$m = 4$ is not prime,so $R$ is false. Thus,$P \wedge Q 	o R$ is false.For option $(A)$,$Q \wedge R 	o P$: If $m$ is prime $(R)$ and $m$ divides $n^2$ $(Q)$,then by Euclid's Lemma,$m$ must divide $n$ $(P)$. This is a standard mathematical theorem. Therefore,$Q \wedge R 	o P$ is true.

For integers $m$ and $n$,both greater than $1$,consider the following three statements:
$P$: $m$ divides $n$
$Q$: $m$ divides $n^2$
$R$: $m$ is prime
Which of the following statements is true?

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For integers $m$ and $n$,both greater than $1$,consider the following three statements:$P$: $m$ divides $n$$Q$: $m$ divides $n^2$$R$: $m$ is primeWhich of the following statements is true?