Question

the counter example of all primenumbers or odd is

Answer 1

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 2

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.

#SPJ6