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.

Answered: Image /qna-images/answer/9a3fba93-65d6-4e62-a0a6-55fce1d44632.jpg

Answered: Define the following sets e and s as…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given the set S = {a,b,c,d} and that a ~ b and d b (i) b~ b (ii) b~d (iii) ad (iv) b~c A. Statements (ii) and (iii) only. B. Statements (i) and (ii) only. O C. Statements (i), (ii), and (iii) only. D. Statements (i), (ii), (iii) and (iv). O E. None of the listed alternatives. Reset Selection Rationale: and d b. Which of the following relations must also be true if is to be an equivalence relation on S? ~ h
1. We are given the sets S and V: S = {Anne, Theo} V {studies, runs, meditates} = (a) Find the Cartesian Product of S and V: S x V (b) A relation R. is a subset of the Cartesian product. Create such a subset RC (S X V) with three elements.
4. Let A = {1,2,3} and B ={6,8,10} and define a relation R from A to B as follows: For all (x,y) € A x B, (x, y) ER means that is an integer. a. Is 2 R 8? b. Is 3 R 6? c. Is (3,10) E R? d. Is (1,6) € R? Write R as a set of ordered pairs. f. Write the domain and the range of R? g. Draw an arrow diagram for R.
This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, RUS = {(x, y) E AXB I (x, y) ER or (x, y) E S} RNS = {(x, y)E AXB| (x, y) ER and (x, y) Es}. Let A = {-2, 2, 3, 5} and B = {2, 3} and define relations R and S from A to B as follows: For every (x, y) E Ax B, x R y - |x| = lyl and xsyex - y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, RU S, and RN s. (Enter your answers as comma-separated lists of ordered pairs.) AXB = R = S = RUS = ROS =
1. How many one-one functions are there from a set with m elements to a set with m elements? 2. We want to choose a leader and a Co-leader from a class with 25 C.S. Major students, 30 Math major students, and 10 Economy major students. The leader is supposed to be a C.S. student or a Math student and the co-leader is supposed to have economy major. In how many different ways can we select these two people from the class?
1. Let A = {a, b, c} and B = {r,s, t, u}. Furthermore, let R = {(a, s), (a, t)}, (b, t) be a relation from A to B. Determine dom R ww and ran R.
..10. Let R be a P.I.D. Let l, e R be l.c.m. of a, bɛ R Show that l, e R is l.c.m. of a and b if and only if l, and l, are associates.
11. Let C= {O, 1, 2) and D = (2, 4, 6, 8) and define a relation R from A to B as follows: For all (x, y) E AXB, %3D %3D y+2 (x, y) e R means that is an integer. a. Is 1 R 2? Is 2 R 8? Is (1, 8) e R? Is (2, 6) e R ? b. Write R as a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram for R.
5. Evaluate each of the following sets, where U = {0, 1, 2, 3, ..., 10} А 3D {0, 1, 2, 3, 4, 5} В 3 {0, 2, 4, 6, 8, 10} C = {2, 3, 5, 7}. a. AU B b. ANC с. А'UB d. ANBNC e. A'NBN C f. AU (BN C) h. (AU B')' g. AN (BUC) ј. В — А i. А — В k. А — (В — С) 1. С — (В — A) m. (А — В)N (С — В) n. (А — В)N (А — С)
9.12. Let S = {a, b, c}. Then R = {(a, a), (a, b), (a, c)} is a relation on S. Which of the properties reflexive, symmetric and transitive does the relation R possess? Justify your answers.

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