# How to proof this?

• Oct 11th 2009, 05:32 AM
MaryB
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(Hi)
• Oct 11th 2009, 05:50 AM
Plato
Quote:

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.
• Oct 11th 2009, 06:33 AM
MaryB
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 :)
• Oct 11th 2009, 07:26 AM
MaryB
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?