Suppose X is a fixed natural number. Let O represent the statement: "X is an odd number" and P represent the statement: " X is a prime ". Use logical connectives and quantifiers to express the following statement: "A necessary condition for x to be odd is that x is a prime." P-O O-P OP40 None of above.
Suppose X is a fixed natural number. Let O represent the statement: "X is an odd number" and P represent the statement: " X is a prime ". Use logical connectives and quantifiers to express the following statement: "A necessary condition for x to be odd is that x is a prime." P-O O-P OP40 None of above.
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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![**Logical Expressions and Quantifiers**
Suppose \( X \) is a fixed natural number. Let \( O \) represent the statement: " \( X \) is an odd number" and \( P \) represent the statement: " \( X \) is a prime". Use logical connectives and quantifiers to express the following statement:
"A necessary condition for \( X \) to be odd is that \( X \) is a prime."
**Answer Choices:**
- \( P \rightarrow O \)
- \( O \rightarrow P \)
- \( P \leftrightarrow O \)
- None of above.
[Note: There are no graphs or diagrams in the given image.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd76a2d57-02e6-4734-ba8a-6fadc8c476a5%2F0ccee895-0fc8-4c08-aec1-669e7352df85%2F96rjd7q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Logical Expressions and Quantifiers**
Suppose \( X \) is a fixed natural number. Let \( O \) represent the statement: " \( X \) is an odd number" and \( P \) represent the statement: " \( X \) is a prime". Use logical connectives and quantifiers to express the following statement:
"A necessary condition for \( X \) to be odd is that \( X \) is a prime."
**Answer Choices:**
- \( P \rightarrow O \)
- \( O \rightarrow P \)
- \( P \leftrightarrow O \)
- None of above.
[Note: There are no graphs or diagrams in the given image.]
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