Question

10. State whether the following sentences are true (T) or false :
I. Every natural number is either prime or composite.
ii. Every prime number is odd.
iii. The sum of primes cannot be a prime.
iv. The product of primes cannot be a prime.
v. A number and its successor are always co-prime. ​

Answer 1

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( i ) False -

So 1 is neither prime nor composite, and this means that regardless of the definition of natural numbers that we use (in other words, whether the definition does nor does not includes 0) it is false that all natural numbers are either prime or composite.

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( ii) By definition a prime number has only 2 factors - itself and 1. Hence the smallest natural prime number is 2, and the only on that is even. All other prime numbers are odd, and there are infinitely many prime numbers.

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( iii ) True

One fact that has been proved is that Every Number is the Product of Prime Numbers is just one way.However, we cannot find two primes with a sum of 27. Because all primes except 2 are odd, adding two primes none of which is 2, is odd+odd which must be even.

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( iV ) True

The product of primes cannot be a prime. An even number is composite.Odd numbers cannot be written as sum of primes. A number and its successor are always co-primes.

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(V) True

If we have a number and its successor than they always co prime . As 2 and its successor 3 is only divisible by 1 , so they are co prime . 99 and its successor 100 have common divisor is 1 , so they are co prime . We can say that a number and its successor is always co-prime.

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$\bf\blue{Hope\ it\ helps.}$

Brainliest Plz.