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### Consider statements \( p \) and \( q \). **\( p \)**: The bench is in the park. **\( q \)**: A tree branch is above us. **(a) Write each statement below in symbolic form using \( p \) and \( q \).** #### Descriptive form **Statement 1:** If a tree branch is not above us, then the bench is in the park. **Symbolic form:** \(\neg q \rightarrow p\) **Statement 2:** A tree branch is not above us and the bench is not in the park. **Symbolic form:** \(\neg q \land \neg p\) **(b) Complete the truth table below. Use T for true and F for false. You may add more columns. But those added columns will not be graded.** **Truth Table:** | \( p \) | \( q \) | \(\neg q\) | \(\neg q \rightarrow p\) | \(\neg p\) | \(\neg q \land \neg p\) | |---------|---------|------------|------------------------|------------|-------------------------| | T | T | F | T | F | F | | T | F | T | T | F | F | | F | T | F | F | T | F | | F | F | T | F | T | T |

### Consider statements \( p \) and \( q \). **\( p \)**: The bench is in the park. **\( q \)**: A tree branch is above us. **(a) Write each statement below in symbolic form using \( p \) and \( q \).** #### Descriptive form **Statement 1:** If a tree branch is not above us, then the bench is in the park. **Symbolic form:** \(\neg q \rightarrow p\) **Statement 2:** A tree branch is not above us and the bench is not in the park. **Symbolic form:** \(\neg q \land \neg p\) **(b) Complete the truth table below. Use T for true and F for false. You may add more columns. But those added columns will not be graded.** **Truth Table:** | \( p \) | \( q \) | \(\neg q\) | \(\neg q \rightarrow p\) | \(\neg p\) | \(\neg q \land \neg p\) | |---------|---------|------------|------------------------|------------|-------------------------| | T | T | F | T | F | F | | T | F | T | T | F | F | | F | T | F | F | T | F | | F | F | T | F | T | T |

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Consider statements \( p \) and \( q \). **\( p \)**: The bench is in the park. **\( q \)**: A tree branch is above us. **(a) Write each statement below in symbolic form using \( p \) and \( q \).** #### Descriptive form **Statement 1:** If a tree branch is not above us, then the bench is in the park. **Symbolic form:** \(\neg q \rightarrow p\) **Statement 2:** A tree branch is not above us and the bench is not in the park. **Symbolic form:** \(\neg q \land \neg p\) **(b) Complete the truth table below. Use T for true and F for false. You may add more columns. But those added columns will not be graded.** **Truth Table:** | \( p \) | \( q \) | \(\neg q\) | \(\neg q \rightarrow p\) | \(\neg p\) | \(\neg q \land \neg p\) | |---------|---------|------------|------------------------|------------|-------------------------| | T | T | F | T | F | F | | T | F | T | T | F | F | | F | T | F | F | T | F | | F | F | T | F | T | T |
Transcribed Image Text:### Consider statements \( p \) and \( q \). **\( p \)**: The bench is in the park. **\( q \)**: A tree branch is above us. **(a) Write each statement below in symbolic form using \( p \) and \( q \).** #### Descriptive form **Statement 1:** If a tree branch is not above us, then the bench is in the park. **Symbolic form:** \(\neg q \rightarrow p\) **Statement 2:** A tree branch is not above us and the bench is not in the park. **Symbolic form:** \(\neg q \land \neg p\) **(b) Complete the truth table below. Use T for true and F for false. You may add more columns. But those added columns will not be graded.** **Truth Table:** | \( p \) | \( q \) | \(\neg q\) | \(\neg q \rightarrow p\) | \(\neg p\) | \(\neg q \land \neg p\) | |---------|---------|------------|------------------------|------------|-------------------------| | T | T | F | T | F | F | | T | F | T | T | F | F | | F | T | F | F | T | F | | F | F | T | F | T | T |
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