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Question

# State true (T) of false (F):(i) The sum of primes cannot be a prime.(ii) The product of primes cannot be a prime.(iii) An even number is composite.(iv) Two consecutive numbers cannot be both primes.(v) Odd numbers cannot be composite.(vi) Odd numbers cannot be written as sum of primes.(vii) A number and its successor are always co-primes.

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Solution

## (i) The sum of primes cannot be a prime.Ex: 2+3=5 which is a prime number.So, the given statement is False.(ii) The product of primes cannot be a prime.Since, in the product of two primes, those two primes also factors of the product.So, The product of prime numbers is always a composite number.Ex: 7×5=35Factors of 35 are 1,5,7 and 35.So it is a composite number.So, the given statement is True.(iii) An even number is composite.The even number 2 is not a composite number.So, the given statement is False.(iv) Two consecutive numbers cannot be both primes.2 and 3 are consecutive numbers and are also prime numbers.So, the given statement is False.(v) Odd numbers cannot be composite.Ex: 9 is an odd number but it is a composite number as its factors are 1,3 and 9.So, the given statement is False.(vi) Odd numbers cannot be written as sum of primes.9 is an odd number9=7+2 where 7 and 2 are prime numbers.So, Odd numbers can be written as sum of primes also.So, the given statement is False.(vii) A number and its successor are always co-primes.Co-primes: The common factor of two numbers is 1.A number and its successor have only one common factor 1.Ex: lets take two consecutive numbers 9 and 10.Factors of 9 =1,3,9Factors of 10 =1,2,5,10 ⇒ common factor of 9 and 10 is 1.So, the given statement is True.

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