Answer
No, it is not a statement. It is self-referential and leads to a paradox.
Work Step by Step
### Problem 17:
**"This sentence is false or 1 + 1 = 3."**
---
### ✅ Determine if it's a **statement**:
A **statement** must be a sentence that is **either true or false**, but not both or undefined.
---
### 🔍 Analysis:
This is a **self-referential** sentence. Let’s call the entire sentence **S**:
> **S**: "S is false or 1 + 1 = 3"
Let’s analyze the truth value:
- The second part, \(1 + 1 = 3\), is **false**.
- So the sentence reduces to:
\[
\text{"This sentence is false"} \lor \text{false}
\Rightarrow S \equiv \text{"S is false"}
\]
So we have:
\[
S \equiv \text{"S is false"}
\]
This is a **liar paradox** — it creates a contradiction:
- If \(S\) is **true**, then it says it is **false** ⇒ contradiction.
- If \(S\) is **false**, then it claims it is **false** ⇒ it is **true** ⇒ contradiction.
---
### ❌ Conclusion:
Because of this contradiction, the sentence does **not** have a well-defined truth value.
