Is this mathematical statement?

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$\{\text{integers $n$ such that $n$ is even}\}$

It can be true/false so does that mean it's proposition/mathematical statement?

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It is only a noun phrase. There is no verb, so it's not a sentence. It can't be true or false.

"Giraffes that are green"

"Giraffes that are green" is not a sentence, but a noun phrase. It cannot be true or false.

"Giraffes that are green are more expensive than elephants." is a complete sentence. It can be true or false.