Consider the poset ({3, 5, 9, 15, 24, 45}, |) under divisibility. Which of the following is correct?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: D. There does not exist a greatest element and a least element
Explanation
No element divides all the others (3 does not divide 5), so there is no least element, and no element is divisible by all the others (45 is not divisible by 24), so there is no greatest element.
More Discrete Structures and Optimisation questions
- How many ways are there to place 8 indistinguishable balls into four distinguishable bins?
- How many bit strings of length ten either start with a 1 bit or end with two bits 00 ?
- Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar represe…
- For which values of and does the complete k bipartite graph m,n have a Hamilton circuit?
- Which of the following is the principal conjunctive normal form of [(p ∨ q) ∧ ¬p] → ¬q?
- How many cards must be selected from a standard deck of 52 cards to guarantee that at least three hearts are present among them?