What are the answers to question 9? (i) Smallest prime number? (ii) Smallest even prime? (iii) Smallest odd prime? (iv) Smallest odd composite?

The first few prime numbers are 2, 3, 5, 7, ...

The smallest prime number is $\boxed{\text{2}}$.

• ii) An even prime number is a prime number that is divisible by 2.

A prime number has exactly two distinct positive divisors: 1 and itself.

Any even number greater than 2 is divisible by 1, 2, and itself, making it composite.

The only even prime number is $\boxed{\text{2}}$.

• iii) The smallest odd prime number is the smallest prime number that is not divisible by 2.

2, 3, 5, 7, ...

The number 2 is even. The next prime number is 3, which is odd.
The smallest odd prime number is $\boxed{\text{3}}$.

• iv) The smallest odd composite number is the smallest natural number greater than 1 that is not prime and is not divisible by 2.

• 2 (prime, even)
• 3 (prime, odd)
• 4 (composite, even, $4 = 2 \times 2$)
• 5 (prime, odd)
• 6 (composite, even, $6 = 2 \times 3$)
• 7 (prime, odd)
• 8 (composite, even, $8 = 2 \times 4$)
• 9 (composite, odd, $9 = 3 \times 3$)

The first composite numbers are 4, 6, 8, 9, ... The smallest odd number in this list is 9.
The smallest odd composite number is $\boxed{\text{9}}$.