MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Let N denote the set of all natural numbers. Define a relation R on N by aRb if and only if a+b is an even integer.
(i) Show that R is reflexive on N.
(ii) Verify that R is symmetric on N.
(iii) Establish that R is transitive on N.
(iv) Conclude whether R is an equivalence relation on N. If it is, write the equivalence class containing the element 3.