Which of the following statements are true?
(i) 1 is the smallest prime number.
(ii) If a number is prime, it must be odd.
(iii) The sum of two prime numbers is always a prime number.
(iv) If two numbers are co-primes, at least one of them must be a prime number.

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Solution

(i) False. 2 is the smallest prime number.
(ii) False. 2 is an even prime number.
(iii) False. 3 and 7 are two prime numbers and their sum is 10, which is even.
(iv) False. 4 and 9 are co-primes but neither of them is a prime number.

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Similar questions

State true (T) of false (F):

$(i)$ The sum of primes cannot be a prime.

$(i i)$ The product of primes cannot be a prime.

$(i i i)$ An even number is composite.

$(i v)$ Two consecutive numbers cannot be both primes.

$(v)$ Odd numbers cannot be composite.

$(v i)$ Odd numbers cannot be written as sum of primes.

$(v i i)$ A number and its successor are always co-primes.

If two numbers are co-primes, at least one of them must be prime.

Statement 1: If two numbers are co-primes, at least one of them must be prime.

Statement 2: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Statement 3: If a number exactly divides two numbers, then it must also divide the sum of both numbers.

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