What is the set complement (A\B) of the following?

[spelawi]

Consider the sets {0}, N, Z, Q and R. Use only the set complement (that is A\B) to describe "the set of all non-positive fractions that have non-zero remainder".

I am so stuck on this question, I can't figure it out.

Please help.

Thank you in advance.

 

[pka]

Consider the sets {0}, N, Z, Q and R. Use only the set complement (that is A\B) to describe "the set of all non-positive fractions that have non-zero remainder".

What in the world does "fractions that have non-zero remainder" mean?
Is that a subset of the irrational numbers?

 

[HallsofIvy]

You have a remainder when you divide. A fraction is an "implied division" so I would guess that means "fractions that are not integers". That set, itself, would be "Q\ Z".

 

[HallsofIvy]

You have a remainder when you divide. A fraction is an "implied division" so I would guess that means "fractions that are not integers". That set, itself, would be "Q\ Z".

 

[pka]

You have a remainder when you divide. A fraction is an "implied division" so I would guess that means "fractions that are not integers". That set, itself, would be "Q\ Z".

That is a really good guess.

But what about the non-positive part?

"the set of all non-positive fractions that have non-zero remainder".

 

[Bob Brown MSEE]

Perhaps Q\N assuming N=set of natural numbers

 

[Bob Brown MSEE]

Consider the sets {0}, N, Z, Q and R. Use only the set complement (that is A\B) to describe "the set of all non-positive fractions that have non-zero remainder".

I am so stuck on this question, I can't figure it out.

Please help.

Thank you in advance.

No Q\N doesn't do it either

 

[pka]

No Q\N doesn't do it either

The OP never answered. So if Halls is correct then this works:
\(\displaystyle [\mathbb{Q}\setminus\{0\}]\setminus\mathbb{N}\).