# Elementary Sets

1. Jul 29, 2009

### avec_holl

1. The problem statement, all variables and given/known data

Let S be a set of Natural numbers with the property that every even number in S is divisible by 5. Which of the following must be true.

a. 2 is not in S
b. 5 is not in S
c. S contains all multiples of 10
d. Every even number in S is divisible by 10
e. S contains no odd numbers

2. Relevant equations

N/A

3. The attempt at a solution

Just want to make sure my logic isn't faltering anywhere so here's what I figured . . .

a. 2 is even, 2 is not divisible by 5, therefore 2 is not a member of S
b. 5 is a natural number, 5 is not even, therefore 5 may be a member of S
c. S does not necessarily contain all multiples of 10
d. Every even member in S must be divisible by 10
e. S may contain odd numbers

Based on this a and d must be true. Thanks!

2. Jul 29, 2009

### n!kofeyn

It looks correct to me! Good job. You might a little more specific on (c) though, as you can give examples of which multiples of 10 the set S cannot contain.

3. Jul 29, 2009

### Dick

I think you've nailed it. Nice work.

4. Jul 29, 2009

### Dick

S might not contain any multiples of 10. It might, in fact, be empty. What would be wrong with that?

Last edited: Jul 29, 2009
5. Jul 29, 2009

### n!kofeyn

Nothing is wrong with that. What I was getting at is that avec_holl should remove the word necessarily from the sentence "S does not necessarily contain all multiples of 10". This is because S does not contain all multiples of 10. For example, if n is a negative integer, then S cannot contain 10n. The way it was originally written says to me that it is possible for S to contain all multiples of 10, but we can't tell.