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Unformatted text preview: McMaster University Department of Computing and Soft ware Dr. W. Kahl COMP SCI 1FC3 Exercise Sheet 7 COMP SCI 1FC3 — Mathematics for Computing 6 February 2009 Exercise 7.1— Partial Orders (a) Show that every totally ordered set is a lattice. (b) Show that every nonempty finite lattice has a least element and a greatest element. (c) Give one example each of an infinite lattice with: (1) neither a least nor a greatest element (2) a least element, but no greatest element (3) a greatest element, but no least element (4) both a least element and a greatest element (d) For each set S among the following sets of rational numbers, prove or disprove that the poset ( S , ≤ ) is wellfounded: (1) { n + 1 m  n ∈ IN ∧ m ∈ + IN } (2) { n 1 m  n ∈ + IN ∧ m ∈ + IN } (3) { n k m  n ∈ + IN ∧ k ∈ IN ∧ m ∈ + IN ∧ k < m } Exercise 7.2 — Equivalence Relations (a) If Θ : A ↔ A is an equivalence relation and F : A ↔ A is total and F ⊆ Θ holds, then F ; Θ = Θ ....
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 Spring '11
 kahl
 Greatest element, Partially ordered set, McMaster University Department of Computing, new Haskell function, Dr. W. Kahl

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