Republic of the Philippines
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
College of Computer and Information Sciences
Sta. Mesa, Manila
Name: Cabale, Johnry S.
Date: 5/5/2025
Course: BSCS 1-1N
Subject: Discrete Mathematics I
COMP 004 Discrete Structures 1
Activity 6: Relations
Instructions. Answer the following statements on a clean sheet of paper or using productivity
tool. Make sure your solution/answer is clear and readable. Submit on MS Teams in pdf format.
1. List the ordered pairs in the relation R from A = {0,1,2,3,4} to B = {0,1,2,3}, where (a,b) ∈ R if
and only if
a) a + b = 4
• R= {(1,3), (2,2), (3,1), (4,0)}
b) a > b
• R= {(1,0), (2,0), (2,1), (3,0), (3,1), (3,2), (4 ,0), (4,1), (4,2), (4,3)}
c) a | b
• R= {(1,1), (1,2), (1,3), (2,2), (3,3)}
d) gcd(a,b) = 1
• R= {(0,1), (1,0), (1,2), (1,3), (2,1), (2,3), (3,1), (3,2), (4,1), (4,3)}
2. For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, symmetric,
anti-symmetric, or transitive.
a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}
• (2,3) and (3,4) → (2,4)∈R
• (2,2), (2,3) → (2,3) already in R
• All needed transitive links are satisfied
• Only Transitive
b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}
• Reflexive = All (a,a) for a ∈ S are included
• Symmetric = (1,2) and (2,1) both in R
• Transitive = (1,2) and (2,1) → (1,1) ∈ R
• Reflexive, Symmetric, Transitive
c) {(2, 4), (4, 2)}
• Symmetric = Each pair has its reverse
• Only Symmetric
d) {(1, 2), (2, 3), (3, 4)}
• Anti-symmetric = No pair (a,b) and (b,a) with a ≠ b
• Only Anti – Symmetric
