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Question 2 How many relations are there on the set A in Question 1? Give the reasoning for your answer. (Answer can be provided in scientific notation). Question 3

Question 2 How many relations are there on the set A in Question 1? Give the reasoning for your answer. (Answer can be provided in scientific notation). Question 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1 Let A be the set A = {3, 4, 8, 9, 12, 24, 54). Determine whether the following relationships are (1) transitive, (2) reflexive, and (3) symmetric or anti-symmetric. Provide the set for each relation on the set A. a. R = {(a, b) a divides b} b. R = {(a, b) a < b + 1} c. R = {(a, b) a - b ≥ 2} d. R = {(a, b) a + b ≤ 10} Question 2 How many relations are there on the set A in Question 1? Give the reasoning for your answer. (Answer can be provided in scientific notation). Question 3 Which relations in Question 1 (a-d) form a partially ordered set (poset) with the set 4? Why? Provide the original directed graph and the Hasse diagram for the poset(s).
Transcribed Image Text:Question 1 Let A be the set A = {3, 4, 8, 9, 12, 24, 54). Determine whether the following relationships are (1) transitive, (2) reflexive, and (3) symmetric or anti-symmetric. Provide the set for each relation on the set A. a. R = {(a, b) a divides b} b. R = {(a, b) a < b + 1} c. R = {(a, b) a - b ≥ 2} d. R = {(a, b) a + b ≤ 10} Question 2 How many relations are there on the set A in Question 1? Give the reasoning for your answer. (Answer can be provided in scientific notation). Question 3 Which relations in Question 1 (a-d) form a partially ordered set (poset) with the set 4? Why? Provide the original directed graph and the Hasse diagram for the poset(s).
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