- #1
mikky05v
- 53
- 0
Homework Statement
this is the original question
prove: [itex]\forall[/itex] c [itex]\in[/itex] Z, a≠ 0 and b both [itex]\in[/itex] Z$
a|b ⇔ c*a|c*b
Then he corrected himself by saying for problem 1: to show that ca | cb implies a | b ... you must assume c NOT = 0 and invoke "Cancellation Property" of Z.
This kind of confused me but i think I get what he means
The attempt at a solution
so I understand that If you have that ca | cb that's like saying that ac=cbq for some q∈ℤ so, if c≠0 you can just take out those c in the both sides of the expression(because of "Cancellation Property" as he said) and you got left a=bq which means that a|b
my problem is how do I translate this into a formal proof if and only if proof.
this is the original question
prove: [itex]\forall[/itex] c [itex]\in[/itex] Z, a≠ 0 and b both [itex]\in[/itex] Z$
a|b ⇔ c*a|c*b
Then he corrected himself by saying for problem 1: to show that ca | cb implies a | b ... you must assume c NOT = 0 and invoke "Cancellation Property" of Z.
This kind of confused me but i think I get what he means
The attempt at a solution
so I understand that If you have that ca | cb that's like saying that ac=cbq for some q∈ℤ so, if c≠0 you can just take out those c in the both sides of the expression(because of "Cancellation Property" as he said) and you got left a=bq which means that a|b
my problem is how do I translate this into a formal proof if and only if proof.