This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the answers to question 9: i)* The smallest prime number is the smallest natural number greater than 1 that has no positive divisors other than 1 and itself. Step 1: Identify prime numbers. The first few prime numbers are 2, 3, 5, 7, ... Step 2: Find the smallest among them. The smallest prime number is 2. ii)* An even prime number is a prime number that is divisible by 2. Step 1: Recall the definition of a prime number. A prime number has exactly two distinct positive divisors: 1 and itself. Step 2: Consider even numbers. Any even number greater than 2 is divisible by 1, 2, and itself, making it composite. Step 3: The only even number that is prime is 2, as its only divisors are 1 and 2. The only even prime number is 2. iii)* The smallest odd prime number is the smallest prime number that is not divisible by 2. Step 1: List prime numbers: 2, 3, 5, 7, ... Step 2: Identify the first odd prime number. The number 2 is even. The next prime number is 3, which is odd. The smallest odd prime number is 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. Step 1: List natural numbers greater than 1 and classify them as prime or composite, and even or odd. • 2 (prime, even) • 3 (prime, odd) • 4 (composite, even, 4 = 2 × 2) • 5 (prime, odd) • 6 (composite, even, 6 = 2 × 3) • 7 (prime, odd) • 8 (composite, even, 8 = 2 × 4) • 9 (composite, odd, 9 = 3 × 3) Step 2: Identify the smallest composite number that is also odd. The first composite numbers are 4, 6, 8, 9, ... The smallest odd number in this list is 9. The smallest odd composite number is 9. Send me the next one 📸