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.
a. (i) Show that R is reflexive on N.
b. (ii) Verify that R is symmetric on N.
c. (iii) Establish that R is transitive on N.
d. (iv) Conclude whether R is an equivalence relation on N. If it is, write the equivalence class containing the element 3.