# Thread: 2 problems involving examples and counter-examples.

1. ## 2 problems involving examples and counter-examples.

1. if a doesn't divide b and a doesn't divide c , then a doesn't divide b times c.

give a counterexample to show this is a false statement.

2. if a divides c and b divides c sometimes, a times b divides c and sometimes it doesn't

show an example when a times b divides c .

show and example when a times b doesn't divide c.

2. Originally Posted by lonestarross
1. if a doesn't divide b and a doesn't divide c , then a doesn't divide b times c.

give a counterexample to show this is a false statement.

.
a can't be divided by $\displaystyle i$, and a can't be divided by $\displaystyle -i$, but a can be divided by $\displaystyle i . -i$
Note that $\displaystyle i= \sqrt{-1}$
I'm not 100% positive with my answer though

3. You know of a numerical example of this?

4. Originally Posted by lonestarross
1. if a doesn't divide b and a doesn't divide c , then a doesn't divide b times c.

give a counterexample to show this is a false statement.

2. if a divides c and b divides c sometimes, a times b divides c and sometimes it doesn't

show an example when a times b divides c .

show and example when a times b doesn't divide c.
Usually with this language and nothing else specified, we assume we are working over the integers.

(1) is very simple.. don't know how to give a hint, here's such a counterexample, learn from it

a = 2*3
b = 2*5
c = 3*5

(2) this is confusing. Is the first part supposed to mean

if (a divides c) and (b divides c sometimes)

or

if (a divides c and b divides c) sometimes

?

I'll assume the first. But it can be proven with the stricter requirement "a divides c and b divides c always".

Just use simple examples. For the case ab divides c, let c = ab. For ab does not divide c, let a = b = c > 1.

5. the first.\\ but when you say a=2*3, b=2*5, c=3*5, 5 does divide 10 and 15...never mind i t is backwards

6. Originally Posted by lonestarross
the first