TRUE or FALSEDO NOT COPY FROM OTHER WEBSITESUpvote guarenteed for a correct and detailed answer. Thank you!!! **Concept Explanation:**2. If \( n \) is a prime number, it is possible that \( n! + 1 \) is not prime.**Detailed Analysis:**- **Prime Numbers:** Numbers greater than 1 that have no divisors other than 1 and themselves. - **Factorial (n!):** The product of all positive integers up to \( n \). For example, \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \).**Understanding the Statement:**The statement discusses the nature of the expression \( n! + 1 \) when \( n \) is a prime number. The factorial of a number \( n \), especially when \( n \) is large, results in a large product. Adding 1 might intuitively seem like it could easily be prime, but this is not always the case.**Examples:**- For \( n = 5 \), \( n! = 120 \) and \( n! + 1 = 121 \), which is \( 11 \times 11 \), not a prime number. - For \( n = 7 \), \( n! = 5040 \) and \( n! + 1 = 5041 \), which is \( 71 \times 71 \), not a prime number.These examples illustrate that although \( n \) is a prime, \( n! + 1 \) may not be a prime.**Conclusion:**When working with such expressions involving factorials, it is essential to check for primality, as assumptions based on simpler scenarios can be misleading.

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Answered: 2. If n is a prime number, it is…

2. If n is a prime number, it is possible that n! + 1 is not prime.

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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