Consider the Following Relations On $\{ 1,2,3 \}$ (A) Which of These Relations Are Reflexive? Justify Your Answers

question 4

Essay

Consider the following relations on $\{ 1,2,3 \}$ .
$$\begin{array} { l } R _ { 1 } = \{ ( 1,1 ) , ( 1,3 ) , ( 2,2 ) , ( 3,1 ) \} \\R _ { 2 } = \{ ( 1,1 ) , ( 2,2 ) , ( 3,1 ) , ( 3,3 ) \} \\R _ { 3 } = \{ ( 1,2 ) , ( 2,1 ) , ( 3,3 ) \} \\R _ { 4 } = \{ ( 1,3 ) , ( 2,3 ) \}\end{array}$$
(a) Which of these relations are reflexive? Justify your answers.
(b) Which of these relations are symmetric? Justify your answers.
(c) Which of these relations are antisymmetric? Justify your answers.
(d) Which of these relations are transitive? Justify your answers.

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Definitions:

Diversity

The presence of differences within a given setting, including race, ethnicity, gender, age, and other attributes affecting personal experiences and perspectives.

Cohesiveness

Refers to the degree of closeness and solidarity among members of a group.

Group Cohesiveness

The extent to which members of a group feel connected and committed to each other and to the group's objectives.

Threat

A perceived danger or harm that may negatively affect an individual's or organization's well-being.