Define the following sets e and s as follows:e = {Devin, Elsa, Floyd}, s = {Software 1, Software 2, Software 3, Software 4}Relation L: els if employee e has software s loaded on their machineL = {(Devin, Software 2), (Elsa, Software 1), (Elsa, Software 3), (Elsa, Software 4), (Floyd, Software 1),(Floyd, Software 3), (Floyd, Software 4)}1. Create an arrow diagram for the relation.2. Create a matrix representation for the relation.

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Answered: Define the following sets e and s as…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.1: Sets

Problem 33E

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B. Represent the following relations as indicated. 1) F= {(1, b), (4, c), (5, c), (1, d)}; as a table 2) R= {(me, you), (me, I), (you, me), (I, we)}; as an arrow diagram 3) E= {(1, 1), (2, 8), (3, 27), (4, 64)}; as an equation 4) N = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}; as a verbal statement 5) D = {(1, 2), (3, 4), (4, 5)}; as an inequality
4. Let A = {a,b,c,d}. Suppose R is the relation R = {(a,a), (b, b), (c, c), (d, d),(a, b), (b, a),(a, c), (c,a), (a,d),(d, a),(b, c), (c, b), (b, d),(d, b), (c,d),(d,c)}. Is R reflexive? Symmetric? Transitive? If a property does not hold, say why. 5. Consider the relation R = {(0,0), (√2,0), (0, √2), (√2, √2)} on R. Is R reflexive? Symmetric? Transitive? If a property does not hold, say why.
2. For each of the following relations on the set {1,3,4,7}. • R1 = {(7, 7), (1, 1), (4, 4), (3, 3)} • R2 {(3, 3), (1, 1), (4, 4), (7, 4), (7, 7), (4, 7), (7, 3)} • R3 = {(3,3), (7, 7), (1, 7), (4, 4), (7, 4), (1, 1), (1, 4)} • R4 = {(7,3), (3, 3), (1, 1), (4, 4), (7, 7), (3, 1), (1, 3), (3, 7)} (a) Which of these relations are reflexive? If not, give a counterexample. (b) Which of these are symmetric? If not, give a counterexample. (c) Which of these are anti-symmetric? If not, give a counterexample. (d) Which of these are transitive? If not, give a counterexample. (e) Which of these are partial ordering? If not, explain why not. (f) Which of these are equivalence relations? If not, explain why not. (g) Draw the digraph of R4. (h) R2 o R4 =
8. Let A = {1, 2, 3, 4, 5). (a) Determine, with justification, if the following relation is reflexive. R= = {(1, 1), (1, 2), (3, 1), (2, 2), (5, 4), (4, 4), (5, 5), (3, 2), (3, 4), (2, 5), (2, 1)} (b) Determine, with justification, if the following relation is symmetric. R = {(1, 1), (2, 2), (2, 3), (3, 2), (4, 5), (5, 1), (3, 4), (5, 4), (1, 5), (4,4)} (c) Determine, with justification, if the following relation is antisymmetric. R = {(2, 2), (3, 1), (1, 1), (3, 3), (5, 4), (5, 5), (2, 4), (4, 3), (4,5)} (d) Determine, with justification, if the following relation is transitive. R = {(1, 2), (2, 3), (1, 3), (4, 4), (3, 4), (3, 5), (1, 4), (2,4)}
You create a general AI (artificial intelligence) and want to teach him "friendship" as a relation on a set of people. You define some rules for this friendship relation. These are your four laws of robotic friendships: 1. "Everyone is friend of him or herself". 2. "Not everyone is friend with everyone". 3. "The enemy of my enemy is my friend" (here "enemy" just means "not friend"). 4. "The enemy of my friend is my enemy." a) Can the following directed graph represent the above "friendship" relation on a set of 2 people? Justify your answer. Alice Bob b) Is the defined "friendship" relation reflexive? Justify your answer (explain, in English). c) Is the defined "friendship" relation symmetric? Justify your answer (explain, in English). d) Is the defined "friendship" relation transitive? Justify your answer (explain, in English).

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