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### Logical Reasoning and Symbolic Representation: Statements and Truth Tables #### Consider Statements \( p \) and \( q \): \( p: \) The bench is in the park. \( q: \) A tree branch is above us. --- #### (a) Writing Each Statement in Symbolic Form | **Descriptive Form** | **Symbolic Form** | |--------------------------------------------------------------------|-----------------------| | **Statement 1:** If a tree branch is not above us, then the bench is in the park. | \(\neg q \rightarrow p\) | | **Statement 2:** A tree branch is not above us and the bench is not in the park. | \(\neg q \land \neg p\) | --- ### (b) Completing the Truth Table Use \( T \) for true and \( F \) for false. You may add more columns, but those added columns will not be graded. Below the table, there is a small graphic depicting the addition of columns, implying that you can expand the table further for more detailed analysis. By following these instructions and understanding the symbolic forms, you will be better equipped to think logically and reason with statements using symbolic logic in your studies.

### Logical Reasoning and Symbolic Representation: Statements and Truth Tables #### Consider Statements \( p \) and \( q \): \( p: \) The bench is in the park. \( q: \) A tree branch is above us. --- #### (a) Writing Each Statement in Symbolic Form | **Descriptive Form** | **Symbolic Form** | |--------------------------------------------------------------------|-----------------------| | **Statement 1:** If a tree branch is not above us, then the bench is in the park. | \(\neg q \rightarrow p\) | | **Statement 2:** A tree branch is not above us and the bench is not in the park. | \(\neg q \land \neg p\) | --- ### (b) Completing the Truth Table Use \( T \) for true and \( F \) for false. You may add more columns, but those added columns will not be graded. Below the table, there is a small graphic depicting the addition of columns, implying that you can expand the table further for more detailed analysis. By following these instructions and understanding the symbolic forms, you will be better equipped to think logically and reason with statements using symbolic logic in your studies.

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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### Logical Reasoning and Symbolic Representation: Statements and Truth Tables #### Consider Statements \( p \) and \( q \): \( p: \) The bench is in the park. \( q: \) A tree branch is above us. --- #### (a) Writing Each Statement in Symbolic Form | **Descriptive Form** | **Symbolic Form** | |--------------------------------------------------------------------|-----------------------| | **Statement 1:** If a tree branch is not above us, then the bench is in the park. | \(\neg q \rightarrow p\) | | **Statement 2:** A tree branch is not above us and the bench is not in the park. | \(\neg q \land \neg p\) | --- ### (b) Completing the Truth Table Use \( T \) for true and \( F \) for false. You may add more columns, but those added columns will not be graded. Below the table, there is a small graphic depicting the addition of columns, implying that you can expand the table further for more detailed analysis. By following these instructions and understanding the symbolic forms, you will be better equipped to think logically and reason with statements using symbolic logic in your studies.
Transcribed Image Text:### Logical Reasoning and Symbolic Representation: Statements and Truth Tables #### Consider Statements \( p \) and \( q \): \( p: \) The bench is in the park. \( q: \) A tree branch is above us. --- #### (a) Writing Each Statement in Symbolic Form | **Descriptive Form** | **Symbolic Form** | |--------------------------------------------------------------------|-----------------------| | **Statement 1:** If a tree branch is not above us, then the bench is in the park. | \(\neg q \rightarrow p\) | | **Statement 2:** A tree branch is not above us and the bench is not in the park. | \(\neg q \land \neg p\) | --- ### (b) Completing the Truth Table Use \( T \) for true and \( F \) for false. You may add more columns, but those added columns will not be graded. Below the table, there is a small graphic depicting the addition of columns, implying that you can expand the table further for more detailed analysis. By following these instructions and understanding the symbolic forms, you will be better equipped to think logically and reason with statements using symbolic logic in your studies.
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