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(D) Given $r: q \vee \sim p$.Using the logical equivalence $p \rightarrow q \equiv \sim p \vee q$,we can rewrite the expression:$q \vee \sim p \equiv

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If $X$ is not an isosceles triangle,then $X$ is not an equilateral triangle.

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(D) Given $r: q \vee \sim p$.Using the logical equivalence $p \rightarrow q \equiv \sim p \vee q$,we can rewrite the expression:$q \vee \sim p \equiv \sim p \vee q$.By the contrapositive rule,$\sim p \vee q \equiv \sim q \rightarrow \sim p$.Translating this back into words:$\sim q$: $X$ is not an isosceles triangle.$\sim p$: $X$ is not an equilateral triangle.Thus,$\sim q \rightarrow \sim p$ means: "If $X$ is not an isosceles triangle,then $X$ is not an equilateral triangle."Therefore,Option $(D)$ is correct.

Let $p, q$ and $r$ be the statements:
$p$: $X$ is an equilateral triangle
$q$: $X$ is an isosceles triangle
$r: q \vee \sim p$
Then the equivalent statement of $r$ is:

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Let $p, q$ and $r$ be the statements:$p$: $X$ is an equilateral triangle$q$: $X$ is an isosceles triangle$r: q \vee \sim p$Then the equivalent statement of $r$ is: