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.
Which two given statements are incorrect?
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1,3,4
To determine which two given statements are incorrect, we can analyze each statement one by one.
1. Every prime number is odd.
This statement is incorrect. While it is true that many prime numbers are odd, the number 2 is an exception. 2 is the only even prime number.
2. There are 8 prime numbers between 10 and 40.
To check the accuracy of this statement, we can list the prime numbers between 10 and 40: 11, 13, 17, 19, 23, 29, 31, 37.
As there are indeed 8 prime numbers between 10 and 40, this statement is correct.
3. There are 11 composite numbers between 0 and 20.
To check the accuracy of this statement, we can list the composite numbers between 0 and 20: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.
As there are 11 composite numbers between 0 and 20, this statement is correct.
4. The number 4 is the smallest even composite number.
This statement is correct. The number 4 is indeed the smallest even composite number. A composite number is a positive integer greater than 1 that has at least one divisor (other than 1 and itself). In the case of 4, it is divisible by both 2 and 4.
Based on our analysis, the incorrect statements are:
1. Every prime number is odd.
4. The number 4 is the smallest even composite number.