If `f : Z -> Z,f(x) = x^2`,what are equivalence classes for this equivalence relation ?

If f:Z rarr Z,f(x)=x^(2), what are equivalence classes for this equivalence relation?

Let L be the set of lines in XY plane. Define a relation s in L by xSy x = y or x-Ly or x Il y. Is S an equivalence relation? If so, what are equivalence classes ? What is the equivalence class containing X-axis ? What happens if L is the set of all lines in space?

f:N rarr N,f(x)=x^(2) is a function.We define xsy if f(x)=f(y) .Is S an equivalence relation ? What are equivalence classes?

A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .

Which of the following defined on Z is not an equivalence relation ?

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

Let f: X rarrY be a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)} . Examine whether R is an equivalence relation or not.

Let f: X to Y be a function. Define a relation R in X given by R = {(a,b):f (a) =f (b)}. Examine whether R is an equivalence relation or not.