0.0K/s "0.ll O33% 8:09 PM...4. a. Define the following Terms giving one example each:i. Partial Ordering Relationsii. Equivalence relationsb. Answer these questions for the partial order represented by the following Hassediagram.eaudiSmkrрi. Find the maximal elements.ii. Find the minimal elements.iii. Is there a greatest element?iv. Is there a least element?v. Find all upper bounds of {m, k, s}.vi. Find all lower bounds of {c, d, t}.vii. Find the greatest lower bound of {u, k, m} if it exists.viii.Find the least upper bound of {b, k, t} if it exists.

Example of Partial order is Less equal order on set of real numbers. Example of Equivalence relation…

4. a. Define the following Terms giving one example each: i. Partial Ordering Relations ii. Equivalence relations b. Answer these questions for the partial order represented by the following Hasse diagram. a d' i m k n h i. Find the maximal elements. ii. Find the minimal elements. iii. Is there a greatest element? iv. Is there a least element? v. Find all upper bounds of {m, k, s}. vi. Find all lower bounds of {c, d, t}. vii. Find the greatest lower bound of {u, k, m} if it exists. viii. Find the least upper bound of {b, k, t} if it exists.

4. a. Define the following Terms giving one example each: i. Partial Ordering Relations ii. Equivalence relations b. Answer these questions for the partial order represented by the following Hasse diagram. a d' i m k n h i. Find the maximal elements. ii. Find the minimal elements. iii. Is there a greatest element? iv. Is there a least element? v. Find all upper bounds of {m, k, s}. vi. Find all lower bounds of {c, d, t}. vii. Find the greatest lower bound of {u, k, m} if it exists. viii. Find the least upper bound of {b, k, t} if it exists.

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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4. a. Define the following Terms giving one example each: i. Partial Ordering Relations ii. Equivalence relations b. Answer these questions for the partial order represented by the following Hasse diagram. u Find the maximal elements. ii. Find the minimal elements. iii. Is the iv. Is there a least element? i. a greatest element? v. Find all upper bounds of {m, k, s}. vi. Find all lower bounds of {c, d, t}. vii. Find the greatest lower bound of fu, k, m} if it exists. viii. Find the least upper bound of {b, k, t} if it exists.