Discrete Mathematics Solved Assignment

1
Surname:
Discrete mathematics
Name:
Course:
Instructor’s name
affiliated Institution:
date:

2
Surname:
Discrete mathematics
Question one
1. a. the answer is false
b. the answer is true
c. the answer is false
d. the answer is false
e. the answer is true.
f. it is symmetric
g. it is transitive
h. it is reflexive
i. it is anti-symmetric
j) it satisfies the properties of (f), (g) and (h).
Question two
a) R ∪ S = { (1, 1) (1, 2) (1, 3) (1, 4) (2, 4) (3, 1) (3, 3) (4, 1) (4, 2) (2, 1) (3, 2) (4, 3) (4,
4 ) }
b) R ∩ S = { (1, 2), (2, 4), (3, 1) }
c) Matrix representations of relations
R∧S=
[ 1 1 1 1
1 0 0 1
1 1 1 0
1 1 1 1 ]
R ∘ S = { (1, 2) (1, 1) (1, 2, (1, 3) (2, 4) (3, 2) (3, 2) (4, 2) (4, 1) } (Schmidt, 2012)