Consider the set A = {1, 2, 3, 4}. A relation R on A is given by
R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,4)}.
a. (i) Test whether R is reflexive, symmetric and transitive. Show each verification step clearly.
b. (ii) Determine the smallest number of ordered pairs that must be adjoined to R so that the enlarged relation becomes an equivalence relation on A. List all the additional ordered pairs you have inserted.
c. (iii) Write the final equivalence classes of A under the enlarged relation.