 Hello and welcome to the session, let us understand the following question which says show that the relation r in the set a is equal to x belongs to z such that 0 is less than equal to x is less than equal to 12 given by r is equal to a b such that mod of a minus b is a multiple of 4 is an equivalence relation find the set of all elements related to one in each case. Now let's proceed on to the solution. We have r is equal to a b such that mod of a minus b is a multiple of 4. A b belongs to a is equal to z such that 0 is less than equal to x is less than equal to 12 which is equal to element 0, 1, 2 is equal to c is a multiple of 4 beta for sum alpha beta is equal to plus minus is equal to plus minus 4 alpha plus minus 4 beta. Part of the question says related to a multiple of 4.