Consider the set and define a relation on by R= (a,b) ,| ,a-b is divisible by 5
MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Consider the set B={1,2,3,4,5,6,7,8,9,10} and define a relation R on B by
R={(a,b)∣a−b is divisible by 5}.
(a) Determine the total number of ordered pairs in R.
(b) Prove that the relation R is symmetric.
(c) Decide, with proof, whether R is reflexive and whether it is transitive.