the counter example of all primenumbers or odd is
Answers
A counterexample to the statement "all prime numbers are odd numbers" is the number 2, as it is a prime number but is not an odd number. Neither of the numbers 7 or 10 is a counterexample, as neither contradicts the statement.
1. Brian says all prime numbers are odd. Prove he is incorrect.
2 is a prime number and 2 is even
2. Helen says all odd numbers are prime. Prove Helen is incorrect.
9 is an odd number and 9 is not prime because it has more than 2 factors.
The factors of 9 are 1, 3, 9
3. Colin says if x and y are prime numbers will x2
+ y2 will be an even number. Is he correct?
If x = 3 and y = 5 32
+ 52
= 9 + 25 = 34 34 is even
If x = 11 and y = 7 112
+ 7
2
= 121 + 49 = 170 170 is even
If x = 2 and y = 5 22
+ 52
= 4 + 25 = 29 29 is odd
He is incorrect
4. Sandra says the cube of a number is always larger than its square. Is she correct?
If x = 3 32
= 9 33
= 27 true
If x = 1 12
= 1 13
= 1 false
If x = -2 -2
2
= 4 -2
3
= -8 false
Answer:
A counterexample to the statement "all prime numbers are odd numbers" is the number 2, as it is a prime number but is not an odd number.
Step-by-step explanation:
- The number 2, which is a prime number but not an odd number, serves as a refutation of the claim that all prime numbers are odd numbers. 2 is an even yet prime number.
- Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is a natural number greater than one that is not prime.
- Another counterexample that we can think of to the statement “all prime numbers are odd numbers” is that the number 1, even though an odd number, is not a prime number.
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