Define a relation on the set of real numbers by R= (a,b) R R ,| ,a-b Q
MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Define a relation R on the set of real numbers R by
R={(a,b)∈R×R∣a−b∈Q}.
(i) Prove that R is reflexive.
(ii) Prove that R is symmetric.
(iii) Prove that R is transitive.
(iv) What special type of relation is R? Justify your answer.
(v) Describe explicitly the equivalence class of 2 under this relation.