By Garrett P.

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Express the information you using the formalism of mathematical logic. 44 2 Mathematics Basics 6. ,Jn denote Web pages (or journal papers). ,n). Turn the set of pages (papers) into a poset on their posting date, and then on the length (length is equal to number of words) of their URLs. What do you observe? 7. Let us assume that you are given the task to design an ordered structure for toys in a kindergarten. How would you order the toys? Is there just one way to order them? , to define posets of toys?

17 • {(thought, 1)} is a relation of the Cartesian product {thought} × {1, 2} = {(thought, 1), ((thought, 2)}. , English). , as pairs of corresponding words. 2 Function Let A and B denote two sets. A function f defined over set A with values in set B is a binary relation f ⊆ A × B for which ∀a ∈ A ∃b ∈ B such that afb. The function is usually denoted as f: A → B, f(x) = y, where x ∈ A, y ∈ B. , the mapping of x onto y) is performed, or constructed, falls outside our scope (this generally depends on the application or problem being considered).

Using n = 2 elements, one can form just one lattice. The Hasse diagram of the one 2-element lattice is seen in Fig. 2. Fig. 2. The one 2-element lattice. With n = 3 elements, one can also form just one lattice. The Hasse diagram of the one 3-element lattice is shown above in Fig. 1. Using n = 4 elements, one can form two lattices. The Hasse diagrams of the two 4-element lattices are pictured in Fig. 3. Fig. 3. The two 4-element lattices. The Hasse diagrams of the five 5-element lattices are illustrated in Fig.

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