Need help on questions 1 c),d),e) and 2 and 3 to complete this assignment.

 

 

MATH 1P67: Mathematics for Computer Science Spring 2016 Assignment 4: Relations
Due: Wednesday, July 6, at 19:00 (7:00 pm) 1. Consider the relations R = {(1, 2), (2, 3), (3, 1)} and S = {(2, 1), (3, 2), (1, 3)} on {1, 2, 3}.
a) Show that R is not an equivalence relation.
b) Show that S is not an equivalence relation.
c) Find S â—¦ R.
d) Show that S â—¦ R is an equivalence relation.
e) What are the equivalence classes of S ◦ R? 2. Prove that the relation R = {(x, y) | x − y is an integer} is an equivalence relation on the
set of rational numbers. What is the equivalence class of 0? What is the equivalence class
of 1/2? 3. Use the connectivity relation to find the transitive closure of the following relation:
R = {(a, a), (a, b), (a, c), (b, c), (c, a), (c, b)}
Show each step of the algorithm in your work.

Attachments:

• 1492837888-Assignment4.pdf