# Sheet7 - McMaster University Department of Computing and...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 non-empty 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 well-founded: (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 ....
View Full Document

• Spring '11
• kahl
• Greatest element, Partially ordered set, McMaster University Department of Computing, new Haskell function, Dr. W. Kahl

{[ snackBarMessage ]}

### Page1 / 2

Sheet7 - McMaster University Department of Computing and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online