K Let p, q, and r represent the following simple statements. p: The temperature is above 75°. q: We finished eating. r. We go to the pool. Write the symbolic statement r^(p-q) in words. If the symbolic statement is given without parentheses, statements before and after the most dominant connective should be grouped. Translate into English. Choose the correct sentence below. ... * OA. If we have finished eating, and the temperature is above 75°, then we will go to the pool. OB. We go to the pool, and if the temperature is above 75° then we have finished eating. OC. If we go to the pool, then the temperature is above 75° and we have finished eating. OD. If we go to the pool and the temperature is above 75°, then we have finished eating.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Transcription for Educational Website**

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**Logical Statements and Translation Exercise**

In this exercise, you will learn how to translate symbolic logic into English sentences. 

**Given Statements:**

- **p**: The temperature is above 75°.
- **q**: We finished eating.
- **r**: We go to the pool.

**Task:**

Translate the symbolic statement **r ∧ (p → q)** into an English sentence. The symbolic statement includes logical symbols where:
- **∧** represents "and"
- **→** represents "implies" or "if...then"

Consider the logical precedence when translating the statement, and group the statements around the most dominant connective.

**Choose the correct English sentence from the options below:**

- **A.** If we have finished eating, and the temperature is above 75°, then we will go to the pool.
- **B.** We go to the pool, and if the temperature is above 75°, then we have finished eating.
- **C.** If we go to the pool, then the temperature is above 75° and we have finished eating.
- **D.** If we go to the pool and the temperature is above 75°, then we have finished eating.

*Answer carefully by considering the logical structure of the symbolic expression.*

---
Transcribed Image Text:**Transcription for Educational Website** --- **Logical Statements and Translation Exercise** In this exercise, you will learn how to translate symbolic logic into English sentences. **Given Statements:** - **p**: The temperature is above 75°. - **q**: We finished eating. - **r**: We go to the pool. **Task:** Translate the symbolic statement **r ∧ (p → q)** into an English sentence. The symbolic statement includes logical symbols where: - **∧** represents "and" - **→** represents "implies" or "if...then" Consider the logical precedence when translating the statement, and group the statements around the most dominant connective. **Choose the correct English sentence from the options below:** - **A.** If we have finished eating, and the temperature is above 75°, then we will go to the pool. - **B.** We go to the pool, and if the temperature is above 75°, then we have finished eating. - **C.** If we go to the pool, then the temperature is above 75° and we have finished eating. - **D.** If we go to the pool and the temperature is above 75°, then we have finished eating. *Answer carefully by considering the logical structure of the symbolic expression.* ---
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