Consider the given statements.
1. Every prime number is odd.
2. There are 8 prime numbers between 10 and 40.
3. There are 11 composite numbers between 0 and 20.
4. The number 4 is the smallest even composite number.
Do you have a question?
To determine the accuracy of the given statements, we can analyze each one individually:
1. Every prime number is odd.
To verify this statement, we can recall the definition of a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. By checking the definition, we can determine that the statement is false. The number 2 is a prime number, and it is even.
2. There are 8 prime numbers between 10 and 40.
To validate this statement, we can list the prime numbers between 10 and 40 and count them. The prime numbers in this range are: 11, 13, 17, 19, 23, 29, 31, and 37. Counting these primes, we find that there are indeed 8 prime numbers between 10 and 40. Therefore, the statement is true.
3. There are 11 composite numbers between 0 and 20.
To check this statement, we need to identify the composite numbers between 0 and 20. Composite numbers are natural numbers greater than 1 that are not prime and can be factored into smaller positive integers. By listing the composite numbers between 0 and 20, we find: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, and 20. Counting these numbers confirms that there are indeed 11 composite numbers between 0 and 20. Hence, the statement is true.
4. The number 4 is the smallest even composite number.
To verify this statement, we can list the even composite numbers in ascending order and determine if 4 is the smallest. The even composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, and so on. By examining the list, it is evident that 4 is indeed the smallest even composite number. Therefore, the statement is true.
In summary:
- Statement 1 is false.
- Statement 2 is true.
- Statement 3 is true.
- Statement 4 is true.