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Possible Duplicate:
Simplest Example of a Poset that is not a Lattice

Question is simple

Lattices

A Poset $(S,\leq)$ can be a Lattice if every pair of elements $a,b \in S$ in the Poset has a meet $\exists a \wedge b$ and a join $\exists a \vee b$.

Question 1

Is my definition of lattice correct?

Question2

Is every finite Poset a Lattice?

I guess no, but cannot find an example. Could you please make an example of Poset which is not a Lattice.

  • 1
    A poset with two elements and no nontrivial relations (a two-element antichain) is the minimal counterexample.2012-02-23
  • 0
    Really sorry for creating a duplicate, actually I searched under the lattice-orders label finding no other similar questions.2012-02-23

1 Answers 1