Final answer:
Looking at the given options, option c) 1, 3, 5, 7, includes the only odd integers less than 10 and thus is the correct answer. The correct answer is option C.
Step-by-step explanation:
In order to determine which odd integers less than 10 are prime numbers, we need to first understand what prime numbers are. Prime numbers are numbers that are only divisible by 1 and themselves, with no other factors.
Looking at the given options, option c) 1, 3, 5, 7, includes the only odd integers less than 10 and thus is the correct answer.
When identifying prime numbers less than 10 amongst odd integers, we adhere to the definition that a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The only even prime number is 2, which is not odd, so it's excluded from this list of odd integers.
Assessing Given Options
Let's assess the odd integers less than 10 to determine which are prime:
1 is not a prime number because by definition, a prime number must have exactly two distinct positive divisors: 1 and the number itself. Since 1 only has one divisor, it doesn't meet the prime number criteria.
3 is a prime number because its only divisors are 1 and 3.
5 is a prime number as it can only be divided evenly by 1 and 5.
7 is also prime, with 1 and 7 being its sole divisors.
9, although odd, is not a prime number because it can be divided evenly by 1, 3, and 9.