Suppose a Is the Set Composed of All Ordered Pairs

question 52

Short Answer

Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,
b)R(c,d) means that a + d = b + c.
(a) Prove that R is an equivalence relation.
(b) Find [(2, 4)].

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Definitions:

Theory Perseverance

The phenomenon where individuals maintain their beliefs even in the face of contradictory evidence, often due to the initial formation of a strong impression or belief.

Social Conformity

The act of adjusting one's behaviors, attitudes, or beliefs to align with group norms, often to fit into a society or group.

False Uniqueness

The erroneous belief that one's abilities, thoughts, or characteristics are more unique or exceptional than they actually are, often underestimating commonality with others.

External Attribution

The process of assigning the cause of one's own or others' behaviors to external factors or circumstances beyond the individual's control.