5. Let S be the set of all positive divisors of p²q² where p and q are primes. Consider the poset (S, R) where R is the 'divides' relation, i.e. Vx, y E S, (x, y) E R if x divides y. a) Find a topological sorting for the elements of S. b) What is the greatest element of the poset if there is any ? c) What is the least element of the poset if there is any ?
5. Let S be the set of all positive divisors of p²q² where p and q are primes. Consider the poset (S, R) where R is the 'divides' relation, i.e. Vx, y E S, (x, y) E R if x divides y. a) Find a topological sorting for the elements of S. b) What is the greatest element of the poset if there is any ? c) What is the least element of the poset if there is any ?
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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Let S be the set of all positive divisors of ?^2?^2 where ? and ? are primes. Consider the
poset (S, R) where R is the ‘divides’ relation, i.e. ∀?, ? ∈ ?, (?, ?) ∈ R if x divides y.
a) Find a topological sorting for the elements of S.
b) What is the greatest element of the poset if there is any ? c) What is the least element of the poset if there is any ?
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