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.