`f: N -> 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?

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?

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

If f:X to Y is a function. Define a relation R on X given by R={(a, b): f(a)=f(b)}. Show that R is an equivalence relation on X.

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.

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.

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.

Let f:X->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.

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: N->Z be a function defined as f(x)=x-1000. Show that f is an into function.

Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an into function.