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What is the correct answer to "There are as many equivalence classes as there are which of the following? (Select all that apply.)"? Answer choices in image.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 28E

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What is the correct answer to "There are as many equivalence classes as there are which of the following? (Select all that apply.)"? Answer choices in image.

There are as many equivalence classes as there are which of the following? (Select all that apply.)
distinct horizontal lines in the plane
V distinct integers
distinct real numbers
distinct vertical lines in the plane
O distinct lines in the plane whose coordinates equal each other

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Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.
Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder notation:__________________ (b) In interval notation:__________________
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.