Answer
No, it is not a statement. It is self-referential and logically paradoxical.
Work Step by Step
### Problem 18:
**"This sentence is false and 1 + 1 = 2."**
---
### ✅ Determine if it is a **statement**:
A **statement** is a sentence that is either **true** or **false**, but **not ambiguous** or self-contradictory.
---
### 🔍 Let’s Analyze:
Let’s call the sentence **S**:
> **S**: "S is false and 1 + 1 = 2"
The second part, \(1 + 1 = 2\), is **true**.
So the sentence becomes:
\[
S \equiv \text{"S is false"} \land \text{true} \Rightarrow S \equiv \text{"S is false"}
\]
So again:
\[
S \equiv \text{"S is false"}
\]
This is the **liar paradox** in disguise — it leads to contradiction:
- If \(S\) is **true**, then it claims it is **false** ⇒ contradiction.
- If \(S\) is **false**, then what it says is false, meaning “S is false” is false ⇒ S is **true** ⇒ contradiction.
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### ❌ Conclusion:
This self-referential sentence causes a paradox. It does **not** have a definite truth value, and therefore is **not a statement** in formal logic.
