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Maths-

General

Easy

Question

Let $A$ be the set of all animals. A relation $R$ is defined as $" a R b$ iff $a$ and $b$ are in different zoological parks”. Then $R$ is

Only reflexive
Only symmetric
Only transitive
Equivalence

The correct answer is: Only symmetric

Clearly, $left parenthesis a comma a right parenthesis element of R$ for any $a element of A$
Also,
$left parenthesis a comma b right parenthesis element of R$
$rightwards double arrow a$ and $b$ are in different zoological parks
$rightwards double arrow b$ and $a$ are in different zoological parks
$rightwards double arrow left parenthesis b comma a right parenthesis element of R$
Now, $left parenthesis a comma b right parenthesis element of R$ and $left parenthesis b comma a right parenthesis element of R$ but $left parenthesis a comma a right parenthesis not an element of R$
So, $R$ is not transitive

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