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?

Suppose a box contains a set of n balls (n gt 4) (denoted by B )of four different colours (many have different sizes), viz,red, blue, green and yellow. Show that a relation R defined on B as R={(b_1,b_2) : "balls" b_1 "and" b_2 have the same colour} is an equivalence relation on B. How many equivalence classes can you find with respect ot R ?

Write the equivalence class [3]_7 as a set.

Gram Equivalent || Law OF Equivalence Class Illustrations with Short Tricks

Let R be the equivalence relation on z defined by R = {(a,b):2 "divides" a - b} . Write the equivalence class [0].

If A ={ 1, 2, 3,. . . , 10} R : A to A R = { (a, b) : | a - b| is a multiple of 3} is an equivalence relation, then the equivalence class [1] is

If the relation R in a set of integers defined as R = {(a, b): (a + b) is divisible by 7}, is an equivalence relation, then the equivalence class containing 0 is:

Show that AxxA is an equivalence relation on a non-empty set A. What is the corresponding equivalence class.