Lattice: Exercises

Edited by Kevin Clancy last updated 25th Apr 2017

Try these exercises to test your knowledge of lattices.

Distributivity

Does the lattice meet operator distribute over joins? In other words, for all lattices and all $p, q, r \in L$ , is it necessarily true that $p \land (q \lor r) = (p \land q) \lor (p \land r)$ ? Prove your answer.

Solution

The following counterexample shows that lattice meets do not necessarily distribute over joins.

A non-distributive lattice called as M3

In the above lattice, $p \land (q \lor r) = p \neq t = (p \land q) \lor (p \land r)$ .

Parents:

Lattice (Order Theory)

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AI ALIGNMENT FORUM
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Lattice: Exercises

Distributivity