How to show this mathmatically?

[Kaldanis]

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

Let A and B be sets.
Show that A \ B = ∅ if and only if A ⊆ B.


I think this means that A is a subset of B, therefor if I remove all the elements of A that are in B, A would end up being empty (or ∅).

How do I write this mathmatically or is the above sentence acceptable?

[ArcanaNoir]

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

Let A and B be sets.
Show that A \ B = ∅ if and only if A ⊆ B.


I think this means that A is a subset of B, therefor if I remove all the elements of A that are in B, A would end up being empty (or ∅).

How do I write this mathmatically or is the above sentence acceptable?

You would start with something like, A is a subset of B implies for all x in A, x is in B. ...