Assignment:
Q1. Let A be the set { 1,2,3,4,5,6} and R be a binary relation on A defined as :
{(1,1), (1,3), (1,5), (2,2), (2,6), (3,1), (3,3), (3,5), (4,4), (5,1), (5,3), (5,5), (6,2), (6,6)}
(a) Show that R is reflexive.
(b) Show that R is symmetric.
(c)Show that R is transitive.
Q2. Let A be the set {1,2,3,4,5,6} and let F be the class of subsets of A defined by:
[{1,6}, {2,3,5}, {4}]
(a) Show that F is a partition of A.
(b) Find the equivalence on A determined by F.
(c) Draw the directed graph of the equivalence relation found in part (2).
Provide complete and step by step solution for the question and show calculations and use formulas.