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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=35

Factors 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 number

9=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 =1,3,9

Factors of 10 =1,2,5,10

⇒ common factor of 9 and 10 is 1.

So, the given statement is True.

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