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Q: If some numbers are integers and some integers are prime then all numbers are definitely prime is this a true statement?

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The statement is false.

False

False

false

All primes are integers, but all integers are not prime.

All prime numbers are integers. All integers are rational.

That is false. This type of statement is only true for prime numbers, not for compound numbers such as 6. Counterexample: 2 x 3 = 6

No prime numbers are irrational: All prime numbers are integers, and all integers are rational, since they can be expressed as themselves divided by 1.

Only integers or whole numbers have prime factors.

No, prime numbers are positive integers. Decimals are not prime numbers.

No. Prime numbers are positive integers, and integers are not irrational.

no - prime numbers are integers

No

False.

Since prime numbers are defined as positive integers, any product of prime numbers will be positive.

Prime numbers are integers. They won't equal a decimal.

All integers greater than one are divisible by prime numbers.

Yes.

2 and 3 are the only consecutive integers that are prime numbers.

Yes, they're integers.

The concepts of "prime numbers" and "composite numbers" make sense for integers (whole numbers), not for arbitrary real numbers.

All numbers greater than one are positive integers that are either composite or prime numbers.

No, only natural numbers (positive integers) can be prime.

No - prime numbers are integers - a fraction cannot be a prime number.

The vast majority of rational numbers are not integers. They are numbers which can be written in the form p/q where p and q are integers which are co-prime and q > 1.