輔導案例-COMP9020-Assignment 2

COMP9020 Assignment 2 2019 Term 3 
Due: Sunday, 3rd November, 23:59 
Submission is through WebCMS/give and should be a single pdf file, maximum size 2Mb. Prose should 
be typed, not handwritten. Use of LATEX is encouraged, but not required. 
Discussion of assignment material with others is permitted, but the work submitted must be your own in 
line with the University’s plagiarism policy. 
Problem 1 (20 marks) 
Recall the relation composition operator ; defined as: 
R1; R2 = {(a, c) : there is a b with (a, b) ∈ R1 and (b, c) ∈ R2} 
For any set S, and any binary relations R1, R2, R3 ⊆ S× S, prove or give a counterexample to disprove the 
following: 
(a) (R1; R2); R3 = R1; (R2; R3) (4 marks) 
(b) I; R1 = R1; I = R1 where I = {(x, x) : x ∈ S} (4 marks) 
(c) (R1; R2)← = R←1 ; R 
← 
2 (4 marks) 
(d) (R1 ∪ R2); R3 = (R1; R3) ∪ (R2; R3) (4 marks) 
(e) R1; (R2 ∩ R3) = (R1; R2) ∩ (R1; R3) (4 marks) 
Problem 2 (30 marks) 
Let R ⊆ S× S be any binary relation on a set S. Consider the sequence of r