Answer
Yes, it is a statement. It is vacuously true because the condition is impossible.
Work Step by Step
### Problem 16:
**"All positive integers with negative squares are prime."**
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### ✅ Determine if it's a **statement**:
A **statement** in logic is a sentence that is either **true** or **false**, but **not both** and **not ambiguous**.
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### 🔍 Analysis:
- **"Positive integers with negative squares"** makes no mathematical sense.
- The square of any positive integer is always **positive**.
- So, "positive integers with negative squares" refers to **no actual objects** — the set is empty.
So the sentence is equivalent to:
> "All elements of the empty set are prime."
In logic, a **universal statement** over an **empty domain** is **vacuously true**.
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### ✅ Conclusion:
- It **is** a **statement** (it has a definite truth value).
- It is **true**, but **vacuously true** because the condition applies to nothing.
