Show That the Relation $R = \{ ( x , y ) \mid x - y \text { is an integer } \}$

question 10

Essay

Show that the relation $R = \{ ( x , y ) \mid x - y \text { is an integer } \}$ is an equivalence relation on the set of rational numbers. What are the equivalence classes of 0 and 12 ?

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Definitions:

Supply

The total amount of a good or service available for purchase at any given price level in a given market.

Excess Demand

A situation where the demand for a good or service surpasses its supply at the current price, often leading to price increases.

Quantity Demanded

The total amount of a good or service that consumers are willing and able to purchase at a given price within a certain time period.

Quantity Supplied

The total amount of a good or service that producers are willing and able to sell at a given price over a specific period.