If the successor of a prime number is predecessor of a composite numbe...
To solve this question, we need to understand the concepts of prime numbers and composite numbers.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, 13, etc.
On the other hand, a composite number is a natural number greater than 1 that is not prime, meaning it has at least one divisor other than 1 and itself. Examples of composite numbers include 4, 6, 8, 9, 10, 12, etc.
Let's analyze the given statement step by step:
1. "The successor of a prime number": The successor of a number is the number that comes immediately after it. For example, the successor of 2 is 3, the successor of 5 is 6, etc.
2. "is predecessor of a composite number": The predecessor of a number is the number that comes immediately before it. For example, the predecessor of 3 is 2, the predecessor of 6 is 5, etc.
Now, let's consider the options given:
a) 11: The successor of 11 is 12, but 12 is not a composite number. It is divisible by 2, making it a composite number. Therefore, option 'a' is incorrect.
b) 17: The successor of 17 is 18, and the predecessor of 18 is 17. Here, 18 is a composite number as it is divisible by 2 and 3. Therefore, option 'b' is incorrect.
c) 23: The successor of 23 is 24, and the predecessor of 24 is 23. Here, 24 is a composite number as it is divisible by 2, 3, 4, 6, 8, and 12. Therefore, option 'c' is correct.
d) 29: The successor of 29 is 30, but 30 is not a composite number. It is divisible by 2, 3, 5, and 10, making it a composite number. Therefore, option 'd' is incorrect.
e) None of these: Since option 'c' (23) is the correct answer, option 'e' is incorrect.
Therefore, the correct answer to the question is option 'c' (23).