Let's generalize the situation in problem #1. Consider the relation < on the set [n]%3D{1,2, ... ,n}. Viewing < as a set itself (of ordered pairs), prove that the number of elements in this set(п-1)пis

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Answered: Let's generalize the situation in…

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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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).
You just bought a new car from a dealership that sells cars no older than 2015. Consider therelationship to be the “same age.” The relation is “same age” and the set is cars made in 2015, 2016,2017, 2018, 2019, and 2020. (a) Prove that this relation is an equivalence relation. (b) Describe the partition defined by the equivalence classes
Let A = {3, 4, 5} and B = {5, 6, 7}, and let S be the "divides" relation from A to B. That is, for every ordered pair (x, y) E Ax B, x Sy x|y. Which ordered pairs are in S and which are in S-? (Enter your answers in set-roster notation.) {1} S = %3D S-1
Consider the following two statements: (1) If a relation on a nonempty set is reflexive, then it is not irreflexive. (2) If a relation on a nonempty set is not reflexive, then it is irreflexive O Neither (1) nor (2) is always true. O Only (1) is always true. O Only (2) is always true. Both (1) and (2) are always true.
I am having trouble working thru this problem, any help would be appreciated.
Suppose A and B are two finite sets such that |B| = |A| - 1 and the number of relations on A is 512. Determine: |B|: Number of relations from B to A:

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Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}. Viewing < as a set itself (of ordered pairs), prove that the number of elements in this set (n-1)n