Equivalence class and equivalence relation, Mathematics

1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y).

(a) Prove that R is an equivalence relation on Z.

(b) If for every x ? Z, the equivalence class of x, [x], contains exactly one element, what can be said about the function f?

Posted Date: 3/30/2013 4:02:12 AM | Location : United States







Related Discussions:- Equivalence class and equivalence relation, Assignment Help, Ask Question on Equivalence class and equivalence relation, Get Answer, Expert's Help, Equivalence class and equivalence relation Discussions

Write discussion on Equivalence class and equivalence relation
Your posts are moderated
Related Questions

Simple Random Sampling It refers to the sampling technique whether each and every item of the population is described an equal chance of being included in the sample. Because s

Prove that if f and g are functions, then f intersect g is a function by showing f intersect g = glA A={x:g(x)=f(x)}

1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o


Solve 9 sin ( 2 x )= -5 cos(2x ) on[-10,0]. Solution At first glance this problem appears to be at odds with the sentence preceding the example. However, it really isn't.

different types of rectilinear figures

Describe Order of Operations with example? The order of operations is a set of rules that describe the order in which math operations are done. Try doing this math problem:

the cost of paint used in a redecorating job is $65.70 .This is a reduction from its original cost of $82.13 .What is the percent decrease in the cost of paint to the nearest perce

write a definition for associative property of multiplication in your own words and explain how you use it to compute 4*25*27 mentally