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8.3 Representing Relations

8.3 Representing Relations. Consider the following relations on A={1,2,3,4}. Consider the matrix M 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?. Express in other formats.

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8.3 Representing Relations

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  1. 8.3 Representing Relations

  2. Consider the following relations on A={1,2,3,4} Consider the matrix MR1= | 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 matrix MR1= | 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 matrix MR1= | 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– MR5R6 = MR5 v MR6 Consider the matrices: MR5= and MR6= Find MR R6= MR5 v MR6

  10. Find MR5∩R6 = MR5 ^ MR6 Consider the matrices: MR5= and MR6= Find MR5∩R6 = MR5 ^ MR6

  11. Find MR6°R5 = MR5 MR6(note order)note: the Boolean symbol has a dot in a circle Consider the matrices: MR5= and MR6= Find MR6 °R5 = MR5 MR6 (note order)

  12. More ex Consider MR1 and MR7= |0 0 0 1| |0 0 1 0 | |0 1 0 0 | |1 0 1 1 | Find MR1R7 Find MR1∩R7

  13. More ex Consider MR1 and MR7= |0 0 0 1| |0 0 1 0 | |0 1 0 0 | |1 0 1 1 | Find MR7 ο R1 = MR1 MR7

  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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