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Deveno
Deveno is offline
#4
Feb15-12, 02:47 PM
Sci Advisor
P: 906

Intro to Abstract Math Question about divison of integers.


Quote Quote by blastoise View Post
It's false, because you when you say if and only if it is the same things as

If-And-Only-If Proofs
Often, a statement we need to prove is of the form
\X if and only if Y ." We are then required to do
two things:
1. Prove the if-part: Assume Y and prove X.
2. Prove the only-if-part: Assume X, prove Y .

taken from http://infolab.stanford.edu/~ullman/...es/slides1.pdf

Did 1.

But, number 2 is
Assume n is divisible by b and n is divisible by a if n is divisible by ab


Choose n = 8, b = 2 a = 3
n is divisible by b and n is divisible by a but n is not divisible by ab

so it's false
thx norwegian i see what you mean
8 is not divisible by 3.

let's pick a better example, where a and b have "some factor in common".

so suppose a = 6, and b = 15, and n = 30. then a|n (because 30 = 6*5), and b|n (because 30 = 15*2), but it's pretty obvious ab = 90 does NOT divide 30 (for one, it's bigger).

in general, you only know that n is divisible by the least common multiple of a and b. in our example above, lcm(6,15) = 30, and indeed 30 divides 30.