What is a counterexample to all prime numbers are odd?

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 of them are enough to contradict the statement.

Is 2 a prime number4?

Any number greater than 2 which is a multiple of 2 is not a prime, since it has at least three divisors: 1 , 2 , and itself. (This means 2 is the only even prime.) Any number greater than 3 which is a multiple of 3 is not a prime, since it has 1 , 3 and itself as divisors.

Do all prime numbers have exactly 2 factors yes or no?

Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.

What is 2 A prime or composite?

Since the divisors of 2 are 1 and 2, there are exactly two distinct divisors, so 2 is prime. Rebuttal: Because even numbers are composite, 2 is not a prime.

How is 2 a prime number?

The number 2 is prime. But if a number is divisible only by itself and by 1, then it is prime. So, because all the other even numbers are divisible by themselves, by 1, and by 2, they are all composite (just as all the positive multiples of 3, except 3, itself, are composite).

Which number is a factor of every prime number?

A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13.

How many counterexamples does it take to prove a proposition is true?

To prove a proposition is true, all cases must be proven, but it only takes one counterexample to prove a proposition is false. To unlock this lesson you must be a Study.com Member. Are you a student or a teacher?

What is an example of a counterexample for odd numbers?

For an example from algebra, we can consider the proposition, ‘All prime numbers are odd.’ This one would seem difficult to disprove, as even numbers are always divisible by 2, and therefore, they are composite (not prime). A counterexample for this statement would be the number 2.

What is a counterexample in geometry?

Lesson Summary. Let’s review. A counterexample is an example that disproves a proposition. Counterexamples exist all around us in the world and are often used in mathematics to prove propositions are false. Counterexamples are important to geometry for proving conditional statements false.

Which phrase is true for all natural numbers n?

So this proposition asserts that the final phrase is true for all natural numbers n. That phrase is actually a proposition in its own right: “n2+n+41 is a prime number” In fact, this is a special kind of proposition called apredicate, which is a proposition whose truth depends on the value of one or more variables.