4. a. Define the following Terms giving one example each: i. Partial Ordering Relations ii. Equivalence relations

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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.
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