# Thread: How to proof this?

1. ## How to proof this?

Hi there! I've got a question.

You have got:
X and Y are non empty sets.
You know that the set {Ai} for i in Y is a family of equivalence relations on X, indexed by Y.

How can you show that the set {q | q in Ai for all i in Y} is an equivlance relation on X?

Bye!
Mary

2. Originally Posted by MaryB
X and Y are non empty sets.
You know that the set {Ai} for i in Y is a family of equivalence relations on X, indexed by Y. How can you show that the set {q | q in Ai for all i in Y} is an equivlance relation on X?
There seems to be something wrong with the way you have written the question.
Any relation is set of ordered pairs.
The given set is a set of sets of ordered pairs. I am not sure what to make of that?
Morever, in order to have an equivalence relation we need a relationship between the members of each pair.

Perhaps you could post the question exactly as it appears in you assignment.

3. Sorry, here is the whole assignment:
Let X and Y be non empty sets.
Let {Ai} i in Y be a family of equivalence relations on X, indexed by Y.
Show that {q | q in Ai for all i in Y} is an equivalence relation on X.

That's it

4. Never you mind, there is a piece missing!

My teacher copied it for me, but she did it wrong so there is some information missing.
Can I delete a question?