Given that the set X = 1, 2, 3, 5, 6, 10, 15, 30) and Poset...

Given that the set X = 1, 2, 3, 5, 6, 10, 15, 30) and Poset (X, ≼).
The relation ≼ is defined as follows:
(x, y X) x ≼ y ↔ x factor of y

Question
i). Draw a Hasse diagram of the Poset.
ii). Specify maximum, Maximum, Minimum, Minimum (if any) elements
iii). Is the relation "≼" a Lattice? Explain !

Expert Solution

SOL:

venereology answered 1 year ago

Let X = {1, 2, 3, 4, 5, 6} and let ∼ be given by {(1,...

Let X = {1, 2, 3, 4, 5, 6} and let ∼ be given by {(1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6),(1, 3),(1, 5),(2, 4),(3, 1),(3, 5), (4, 2),(5, 1),(5, 3)}. Is ∼ an equivalence relation? If yes, write down X/ ∼ .

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