 # A relation R on a nonempty set A is called antisymmetric if, for x and y in A , x R y and y R x together imply x = y . (That is, R is antisymmetric if x ≠ y implies that either x R y or y R x .) Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set ℤ of all integers. Determine ineach case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. x R y if and only if x = 2 y . b. x R y if and only if x = − y . c. x R y if and only if y = x k for some k in ℤ . d. x R y if and only if x &lt; y . e . x R y if and only if x ≥ y . f. x R y if and only if x = | y | . g. x R y if and only if | x | ≤ | y + 1 | . h. x R y if and only if x y ≥ i. x R y if and only if x y ≤ j. x R y if and only if | x − y | = 1 . k. x R y if and only if | x − y | &lt; 1 . ### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
Publisher: Cengage Learning,
ISBN: 9781285463230 ### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
Publisher: Cengage Learning,
ISBN: 9781285463230

#### Solutions

Chapter
Section
Chapter 1.7, Problem 23E
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