Download presentation

Presentation is loading. Please wait.

Published byWayne Lamport Modified about 1 year ago

1
8.3 Representing Relations

2
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 | Express as ordered pairs: Which characteristics does R1 have: RSAT?

3
Express in other formats Consider the matrixM R1 = | 1 1 0 1 | | 0 1 0 0 | | 1 1 1 0 | | 0 1 1 1 | Express R1 in the following formats: Graphical

4
…other formats Consider the matrixM R1 = | 1 1 0 1 | | 0 1 0 0 | | 1 1 1 0 | | 0 1 1 1 | Digraph (directed graphs)

5
Determine whether the following are RSA: M R2 = |1 1 1 0 | M R3 = |1 1 1 0 | M R4 = |1 1 0 1 | |1 1 0 0 ||1 1 0 0 || 0 1 0 0 | |0 0 0 1||1 0 0 0 ||1 0 1 0 | |1 0 1 1 ||0 0 0 0 ||0 1 0 1 | 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 = |0 0 0 1| |0 0 1 0 | |0 1 0 0 | |1 0 1 1 | Find M R1 R7 Find M R1∩R7

13
More ex Consider M R1 and M R7 = |0 0 0 1| |0 0 1 0 | |0 1 0 0 | |1 0 1 1 | 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

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google