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8.3 Representing Relations

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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?

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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

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…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)

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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

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Find General Forms for Each Property Reflexive Symmetric Anti-symmetric

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

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Review 0-1 matrices from sec 3.8

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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

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

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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)

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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

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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

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Do Digraph worksheet

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

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Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

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