The following is a supposed proof of the statement, \"Every natural number that
ID: 3005038 • Letter: T
Question
The following is a supposed proof of the statement, "Every natural number that is not prime is a product of primes." proof: Let n be a natural number. Suppose, by contradiction, that n is not a product of primes. Since n is not prime, it must have a prime divisor other than n and 1. Suppose p, a prime, divides n and n=p*s. By our assumption, p and s cannot be prime. This is a contradiction since p is both prime and not prime. Is this a valid proof? Yes, it is a valid proof by contradiction. Yes, it is a valid direct proof. No, a proof by contradiction must start by assuming that n is the product of primes. No, it starts as a proof by contradiction, but incorrectly negates the conclusion.Explanation / Answer
every natural number other than primes can be expressed as product of primes
eg 8 = 2x2x2 ; 15= 3x5, 24= 2x2x2x3,....
42= 2x3x7 , 84= 2x2x3x7,..........
similarly 36 = 4x9 = 6x6 =12x3,
but each number 4.6,9,12 which are not primes but they are product of primes.
4 = 2x2, 6 = 2x3, 9= 3x3, 12= 2x2x3....................
every natural number is expressed as a product of primes.
option c
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