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8.3 Representing Relations. Consider the following relations on A={1,2,3,4} Consider the matrixM R1 = | 1 1 0 1 | | 0 1 0 0 | | 1 1 1 0 | | 0 1 1 1 |

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Presentation on theme: "8.3 Representing Relations. Consider the following relations on A={1,2,3,4} Consider the matrixM R1 = | 1 1 0 1 | | 0 1 0 0 | | 1 1 1 0 | | 0 1 1 1 |"— Presentation transcript:

1 8.3 Representing Relations

2 Consider the following relations on A={1,2,3,4} Consider the matrixM R1 = | | | | | | | | Express as ordered pairs: Which characteristics does R1 have: RSAT?

3 Express in other formats Consider the matrixM R1 = | | | | | | | | Express R1 in the following formats: Graphical

4 …other formats Consider the matrixM R1 = | | | | | | | | Digraph (directed graphs)

5 Determine whether the following are RSA: M R2 = | | M R3 = | | M R4 = | | | || || | | || || | | || || | R S A R S A R S A T will be in a later section

6 Find General Forms for Each Property Reflexive Symmetric Anti-symmetric

7 Challenge: Can you find a matrix that is both symmetric and anti-symmetric? Neither?

8 Review 0-1 matrices from sec 3.8

9 Matrices– M R5  R6 = M R5 v M R6 Consider the matrices: M R5 = and M R6 = Find M R  R6 = M R5 v M R6

10 Find M R5∩R6 = M R5 ^ M R6 Consider the matrices: M R5 = and M R6 = Find M R5∩R6 = M R5 ^ M R6

11 Find M R6°R5 = M R5   M R6 (note order) note: the Boolean symbol has a dot in a circle Consider the matrices: M R5 = and M R6 = Find M R6 °R5 = M R5   M R6 (note order)

12 More ex Consider M R1 and M R7 = | | | | | | | | Find M R1  R7 Find M R1∩R7

13 More ex Consider M R1 and M R7 = | | | | | | | | Find M R7 ο R1 = M R1   M R7

14 Do Digraph worksheet

15 Determine what properties we would see in a digraph that is: Reflexive Symmetric Anti-symmetric Transitive


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