MAT2612 Assignment 4 (872328) Due 2025

Mat2612
Assignment 4
Unique No: 872328
Due 2025

, Mat2612

Assignment 04

Unique no: 872328



Solutions Based on Chapter 6 Partial Orders And Lattices

Question 1 [6 Marks]

Determine whether the relation Ris a partial order on the set A= R, where aRb⇐⇒ a≤ b.

Solution: A relation Ris a partial order if it is:

• Reflexive: a≤ afor all a∈ R– True.

• Antisymmetric: If a≤ band b≤ a, then a= b– True.

• Transitive: If a≤ band b≤ c, then a≤ c– True.

Hence, Ris a partial order relation on R.

Question 2 [22 Marks]

(2.1) [10 Marks] Draw a Hasse diagram of the lattice D36

Let D36 = { d∈ Z+ : d| 36} = {1 2
, 3, 4, 6, 9, 1, 2 1, 8 3, 6}.

Hasse Diagram shows the divisibility relation with edges from lower to upper if a| band
there’s no element csuch that a < c < band a| c, c| b.

36
/ \
12 18
/\ /\
4 69 6
| /\/ \
2 3 3 3
\/ \ /
1




1