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Relations

Relations. Ch 2 schaum’s , Ch 7 Rosen. Hasse Diagram. Hasse Diagram Example. 4 3 2 1. 4 3 2 1. 4 3 2 1. 4 3 2 1. Hasse Diagrams. Consider the graph for a finite poset ({1,2,3,4},≤) When we KNOW it’s a poset , we can simplify the graph. Called the Hasse diagram.

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Relations

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  1. Relations Ch 2 schaum’s, Ch 7 Rosen CSE 211- Discrete Structures

  2. Hasse Diagram CSE 211- Discrete Structures

  3. Hasse Diagram Example CSE 211- Discrete Structures

  4. 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Hasse Diagrams Consider the graph for a finite poset ({1,2,3,4},≤) When we KNOW it’s a poset, we can simplify the graph Called the Hasse diagram CSE 211- Discrete Structures

  5. Hasse Diagram For the poset ({1,2,3,4,6,8,12}, |) CSE 211- Discrete Structures

  6. Greatest Element Least Element Maximal Element Minimal Element Upper Bound Lower Bound Greatest lower bound Least Upper bound CSE 211- Discrete Structures

  7. Find the lower and upper bounds of the subsets {a, b, c} , {j, h}, and {a, c, d, f}. The upper bounds of {a, b, c} are e, f, j, h and its lower bound is a. There is no upper bounds of {j, h}. And its lower bounds are a, b, c, d, e, f. The upper bounds of {a, c, d, f} are f, h and j. and its lower bound is a. Find the greatest lower bound and the least upper bound of {b, d, g} CSE 211- Discrete Structures

  8. Lattices A partially ordered set in which every pair of elements has both a least upper bound and a greatest lower bound is called a lattice.

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