Question

Let A={1,2,3,4,5,6,7,8}A={1,2,3,4,5,6,7,8}. Define a relation ∼∼ on AA by a∼ba∼b if and only if 33 divides a−ba−b for all a,b∈Aa,b∈A.  1. Find all the pairs (a,b)∈A×A(a,b)∈A×A such that a∼ba∼b. 2. Show that ∼∼ is an equivalence relation on AA. 3.  Find the equivalence classes [2][2] and [3][3].​

Answer 1

Define relation.

Let A and B are only two non-empty set,then A*B is cartesian product of A*B.Then any subset of A*B is known as the relation fromA to B.