Recent content by nikie1o2

Ok, So to show its reflexive i can pick an real numbers? I can say (u,v,w)=(1,1,1) so (1,1,1) R (1,1,1) ?

Homework Statement Consider the set A={(u,v,w) in R^3 : u^2+v^2>0} and define a relation ~ on A by (u,v,w)~(u',v',w') IFF there exists a "k" in R, where k doesn't equal 0: (u',v',w')=(ku,kv,kw) Prove that ~ is an equivalence relation of A Homework Equations I honestly don't know...

Hello, thank you for the warm welcome. I have done equivalence relations before but with just two variables not 4. So i was confused on how to prove the reflexive, symmetric & transitive properties. For reflexive i was thinking if (x,y)R(x,y) then ax^2+by^2=ax^2+by^2- so that is true...

Homework Statement let A,B,C be sets, and let f : A--> B and g : B--> C be functions. The composite function denoted by g o f is a function from A to C defined as follows: Homework Equations g o f(x)=g(f(x)) for every x in A. Prove that if g o f is one-to one, then f is one-to...

In R x R , ley (x,y) [FONT="Palatino Linotype"]R (u,v) if ax^2 +by^2=au^2 + bv^2, where a,b >0. Determine the relation [FONT="Palatino Linotype"]R is an equivalnce relation. Prove or give a counter example