Q1. Consider the relation R on the set of integers as xRy if and only if x<y. Then prove that R is partial order relation.
Question
Q1. Consider the relation R on the set of integers as
xRy if and only if x < y.
Then prove that R is a partial order relation.
Solution
The statement is incorrect. The relation R on the set of integers defined as xRy if and only if x<y is not a partial order relation.
A partial order relation must satisfy three properties: reflexivity (every element is related to itself), antisymmetry (if x is related to y and y is related to x, then x and y are identical), and transitivity (if x is related to y and y is related to z, then x is related to z).
The relation R defined as xRy if and only if x<y does not satisfy the reflexivity property because for an integer x, it is not true that x<x. Therefore, R is not a partial order relation.
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