3. Translate the following English sentence into P. Make sure to include your interpretation key. If no one is taller than Becky, then Becky is taller than everyone.
3. Translate the following English sentence into P. Make sure to include your interpretation key. If no one is taller than Becky, then Becky is taller than everyone.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Translating English Sentences into Predicate Logic
**Task 3:** Translate the following English sentence into predicate logic (P). Be sure to include your interpretation key.
**Sentence:**
"If no one is taller than Becky, then Becky is taller than everyone."
#### Suggested Translation and Interpretation Key
**Translation in Predicate Logic:**
Let \( T(x, y) \) mean "x is taller than y".
\[
\neg \exists x (T(x, \text{Becky})) \rightarrow \forall y (T(\text{Becky}, y))
\]
**Interpretation Key:**
- \( T(x, y) \): "x is taller than y"
- \( \neg \exists x (T(x, \text{Becky})) \): "No one is taller than Becky"
- \( \forall y (T(\text{Becky}, y)) \): "Becky is taller than everyone"
This logical formulation effectively captures the original English statement by using predicates to express relationships between individuals' heights.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff44271d-3d7b-4b53-8233-39e662e87f0d%2F5f5f0be1-b30d-4e61-94ec-7a85057197cf%2Fr13dkv8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Translating English Sentences into Predicate Logic
**Task 3:** Translate the following English sentence into predicate logic (P). Be sure to include your interpretation key.
**Sentence:**
"If no one is taller than Becky, then Becky is taller than everyone."
#### Suggested Translation and Interpretation Key
**Translation in Predicate Logic:**
Let \( T(x, y) \) mean "x is taller than y".
\[
\neg \exists x (T(x, \text{Becky})) \rightarrow \forall y (T(\text{Becky}, y))
\]
**Interpretation Key:**
- \( T(x, y) \): "x is taller than y"
- \( \neg \exists x (T(x, \text{Becky})) \): "No one is taller than Becky"
- \( \forall y (T(\text{Becky}, y)) \): "Becky is taller than everyone"
This logical formulation effectively captures the original English statement by using predicates to express relationships between individuals' heights.
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