Determine which of these relations are symmetric. The variables x, y, x', y' represent integers.O A. xRy if and only if æ + y is positive.O B. x Ry if and only if x = |y|.O C. x Ry if and only if cy is positive.OD. xRy if and only if x – y is positive.E. x Ry if and only if xy > 0.

We have to find symmetric relation from given relations.

Determine which of these relations are symmetric. The variables x, y, x', y' represent integers. A. x Ry if and only if x + y is positive. B. x Ry if and only if æ = |y|. O C. x Ry if and only if æy is positive. O D. æ Ry if and only if x – y is positive. O E. x Ry if and only if ry > 0.

Determine which of these relations are symmetric. The variables x, y, x', y' represent integers. A. x Ry if and only if x + y is positive. B. x Ry if and only if æ = |y|. O C. x Ry if and only if æy is positive. O D. æ Ry if and only if x – y is positive. O E. x Ry if and only if ry > 0.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 2E: 2. In each of the following parts, a relation is defined on the set of all integers. Determine in...

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Question

Determine which of these relations are symmetric. The variables x, y, x', y' represent integers.
O A. xRy if and only if æ + y is positive.
O B. x Ry if and only if x = |y|.
O C. x Ry if and only if cy is positive.
OD. xRy if and only if x – y is positive.
E. x Ry if and only if xy > 0.

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2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric or transitive. Justify your answers. a. if and only if . b. if and only if . c. if and only if for some in . d. if and only if . e. if and only if . f. if and only if . g. if and only if . h. if and only if . i. if and only if . j. if and only if . k. if and only if .