Let P be the set of all people and R be a relation defined on P as describedin the parts a, b, c, and d below. Determine if R has the reflexive, symmetric,antisymmetric, or transitive properties. Assume x and y are arbitrarymembers of P.a. x Ry if x is the sister of y.b. x Ry if x and y have the same father.c. x Ry if x and y have the same mother.d. x R y if x and y have the same paternal grandfather.

Reflexive: A relation R is reflexive on the set S if x, x∈R for all x∈S.Symmetric: A relation R is…

Answered: Let P be the set of all people and R be…

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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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.
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 =
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Question 1 Let A be the set A = {3,4, 8, 9, 12, 24, 54). Determine whether the following relationships are (1) transitive, (2) reflexive, and (3) symmetric or anti-symmetric. Provide the set for each relation on the set A. a. R = {(a, b) a divides b} b. R = {(a,b)| a
14 Part 1 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) = R² | a> b), the greater than relation R₂ = {(a, b) € R2 R3 = {(a, b) € R² | a < b), the less than relation R₁ = [(a, b) ER² | a ≤ b), the less than or equal to relation R5 = {(a, b) € R² | a= b), the equal to relation R₁ = {(a, b) = R² | a b), the unequal to relation For these relations on the set of real numbers, find R₂0 R2. Multiple Choice R4 R3 I az b), the greater than or equal to relation R2 R₁
8. Please answer the question pls ty!
A={1,2,3,4,5,6} and consider the following 3 subsets of A. A = {1,3,5}; A2 = Let {2, 4, 6}; A3 = {3, 6}.
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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