In the set W of whole numbers an equivalence relation R is defined as follows aRb iff both a & ~b leave the same reminder when divided by 5. The equivalence class of 1 is given by.

Step-by-step solution

The relation R is defined on the set of whole numbers W = 0, 1, 2, 3, such that aRb if and only if a b 5 . The equivalence class of an element x , denoted by [x] , is the set of all elements y W such that yRx . For x = 1 , the equivalence class [1] consists of all whole numbers y such that y 1 5 . This means y = 5k + 1 for some non-negative integer k . Substituting values for k = 0, 1, 2, 3, : For k = 0 , y = 5(0) + 1 = 1 . For k = 1 , y = 5(1) + 1 = 6 . For k = 2 , y = 5(2) + 1 = 11 . For k = 3 , y = 5(3) + 1 = 16