(A) Let $m$ Be a Positive Integer Greater Than 2 $R$ Consisting of Those Ordered Pairs of Integers (A, B)

question 21

Essay

(a) Let $m$ be a positive integer greater than 2 . Show that the relation $R$ consisting of those ordered pairs of integers (a, b) with $a \equiv \pm b$ (mod m) is an equivalence relation.
(b) Describe the equivalence classes of this relation where $m$ =4 .

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Definitions:

Collective Unconscious

A concept in Jungian psychology referring to the part of the unconscious mind which is derived from ancestral memory and experience and is common to all humankind.

Sigmund Freud

The founder of psychoanalysis, a theory of personality and therapeutic method that emphasizes unconscious motivations and conflicts.

Karen Horney

A German-American psychoanalyst known for her theories on neurosis, personality, and the importance of social relationships in mental health.

Freudian Theory

Freudian Theory encompasses the ideas proposed by Sigmund Freud, emphasizing unconscious mental processes, sexuality, and the psychological roots of dysfunction.