Let p represent the statement: "Students are happy." Let q represent the statement: "Teachers are happy." Translate the following compound statement into words. ~(pv~q)
Let p represent the statement: "Students are happy." Let q represent the statement: "Teachers are happy." Translate the following compound statement into words. ~(pv~q)
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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![**Propositional Logic Translation**
**Instructions:**
Let \( p \) represent the statement: "Students are happy."
Let \( q \) represent the statement: "Teachers are happy."
Translate the following compound statement into words:
\[ \sim ( p \lor \sim q) \]
**Translation:**
The given compound statement \( \sim ( p \lor \sim q) \) can be translated into words as:
"It is not the case that either students are happy or teachers are not happy."
Alternatively, it can be read as:
"Neither are students happy nor are teachers unhappy."
**Explanation:**
- \( \sim \) represents "not."
- \( \lor \) represents the logical "or."
- The compound statement involves negating the expression inside the parentheses, which denotes the disjunction (or) of two propositions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c6af232-16b9-41b8-861f-7b00c0e5f4df%2F669871b8-4a8c-4177-a395-042c3f3bba60%2Fjvgcpdm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Propositional Logic Translation**
**Instructions:**
Let \( p \) represent the statement: "Students are happy."
Let \( q \) represent the statement: "Teachers are happy."
Translate the following compound statement into words:
\[ \sim ( p \lor \sim q) \]
**Translation:**
The given compound statement \( \sim ( p \lor \sim q) \) can be translated into words as:
"It is not the case that either students are happy or teachers are not happy."
Alternatively, it can be read as:
"Neither are students happy nor are teachers unhappy."
**Explanation:**
- \( \sim \) represents "not."
- \( \lor \) represents the logical "or."
- The compound statement involves negating the expression inside the parentheses, which denotes the disjunction (or) of two propositions.
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