(X is a prime number ant it divides a or it divides b) = (x|ab) is true. Does this imply that "if X is a prime number and p|ab then p|a or p|b is true?

Question

(X is a prime number ant it divides a or it divides b) => (x|ab) is true. Does this imply that "if X is a prime number and p|ab then p|a or p|b is true?

anonymous · Answer

first part is true
since x|a and x|b, and ab is a multiple of a and b, x divides ab

the second part is also true since p is a prime, one of a or b must be a multiple of p in order to be divisible by p

jhonyy9 · Answer

excouz me but if i have understood it right in the first words of exercise there have wrote that X is a prime number --- so than we know that a prime number is prime number because divide just by 1 and by issue 
- so a number  if divide by a and by b so than again by 1 and by issue so than from this resulted sure that this number not can being prime never 

-- looke please the prime number deffinition 

good luck

bye