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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.

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.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 17E: In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A....
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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.
Transcribed Image Text: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.
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