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