Define a Relation $R$ On the Set $\{ 1,2,3,4 \}$ As Follows $$R = \{ ( 1,4 ) , ( 2,3 ) , ( 2,4 ) , ( 4,1 ) , ( 2,1 ) , ( 1,2 ) , ( 3,2 ) \}$$

question 14

Essay

Define a relation $R$ on the set $\{ 1,2,3,4 \}$ as follows:
$$R = \{ ( 1,4 ) , ( 2,3 ) , ( 2,4 ) , ( 4,1 ) , ( 2,1 ) , ( 1,2 ) , ( 3,2 ) \}$$
(a) Is $R$ symmetric? Justify your answer.
(b) Is $R$ transitive? Justify your answer.

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Definitions:

Psychoanalytic Groups

Groups that apply principles of psychoanalysis in a collective setting to explore and address the unconscious motivations and dynamics that influence behavior.

Interpreters

Professionals who convert information from one language into another, facilitating communication between people who do not speak the same language.

Behavior

The actions or reactions of an individual or group in response to external or internal stimuli.

Replacement Hypothesis

A theory that suggests new members or elements within a system replace older ones, often in the context of social groups or ecological systems.