MAT2612 Assignment 04 ACCURATE SOLUTIONS (872328 ) Due 2025

MAT2612

ASSIGNMENT 04

Unique No:872328

Due 2025

, Discrete Mathematics Assignment



Question 1: [6 Marks]
Problem Statement
Determine whether the relation R is a partial order on the set A, where A = R and aRb if
and only if a ≤ b.

Step 1: Define a Partial Order
A relation R on a set A is a partial order if it satisfies:

• Reflexivity: aRa

• Antisymmetry: aRb and bRa ⇒ a = b

• Transitivity: aRb and bRc ⇒ aRc

Step 2: Test Reflexivity
Let a ∈ R. Then a ≤ a is always true. Therefore, the relation is reflexive.

Step 3: Test Antisymmetry
Assume a ≤ b and b ≤ a. Then a = b. Hence, the relation is antisymmetric.

Step 4: Test Transitivity
If a ≤ b and b ≤ c, then a ≤ c. Therefore, the relation is transitive.

Final Answer
The relation R = {(a, b) ∈ R × R | a ≤ b} is a partial order on R.




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