 #1
 5
 0
 Homework Statement:

Assume that f:A—>B and that R is an equivalence relation on B
Define Q to be the set {<x,y> ∈ A X A <f(x),f(y)> ∈ R}
 Relevant Equations:
 Define Q to be the set {<x,y> ∈ A X A <f(x),f(y)> ∈ R}
I can’t understand it.
What does ##\langle f(x), f(y) \rangle \in \mathbb R## mean?Homework Statement:: Assume that f:A—>B and that R is an equivalence relation on B
Define Q to be the set {<x,y> ∈ A X A <f(x),f(y)> ∈ R}
Relevant Equations:: Define Q to be the set {<x,y> ∈ A X A <f(x),f(y)> ∈ R}
I can’t understand it.
f(x)∈ dom(R), f(y)∈ ran(R) and f(x)Rf(y)What does ##\langle f(x), f(y) \rangle \in \mathbb R## mean?
what is arbitrary relation on Ais a binary relation on A
write the formulasreflexive on A, symmetric and transitive
I think that it is not a good idea to use notation for realsWhat does mean?
Ah! I missed that. So what's the difficulty here?f(x)∈ dom(R), f(y)∈ ran(R) and f(x)Rf(y)
Okay, what exactly is stopping you getting started? The rules are you have to show an attempt at a solution.How to prove Q is an equivalence relation on A?
I’m sorry.But I have no ideal how to get start.I can't see the connection between x and y in A, the only connection is in B.But B is another set.
R is an equivalence relation on R iff R is a binary relation on A that is reflexive on A, symmetric and transitive
That's not right. You're told f is a function from A to B, so x and y are in A = dom(f) while f(x) and f(y) are in B = ran(f).f(x)∈ dom(R), f(y)∈ ran(R) and f(x)Rf(y)