Aspire Faculty ID #18600 · Topic: UGC NET Computer Science Dec 2022 Shift II (Paper II) · Just now
UGC NET Computer Science Dec 2022 Shift II (Paper II)

A relation $R$ is defined on ordered pairs of integers as $(x, y) R(u, v)$ if $x < u$ and $y > v$. Then $R$ is

Solution

For reflexive relation, we need
$ (x, y) R(x, y) $

But according to the definition,
$ x < x $ and $ y > y $

Both are false.

So, $R$ is not reflexive.

A partial order relation must be reflexive, antisymmetric, and transitive.
Since $R$ is not reflexive, it is not a partial order.

An equivalence relation must be reflexive, symmetric, and transitive.
Since $R$ is not reflexive, it is not an equivalence relation.

Hence, $R$ is neither a partial order nor an equivalence relation.
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