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Question

In the set $A equals open curly brackets 1 comma blank 2 comma blank 3 comma blank 4 comma blank 5 close curly brackets comma$ a relation $R$ is defined by $R equals open curly brackets open parentheses x comma y close parentheses colon x comma y element of A blank a n d blank x less than y close curly brackets.$ Then, $R$ is

Reflexive
Symmetric
Transitive
None of these

The correct answer is: Transitive

Since $x not less-than x comma$ therefore $R$ is not reflexive
Also, $x less than y$ does not imply that $y less than x$
So $R$ is not symmetric
Let $x blank R blank y$ and $y blank R blank z.$ Then, $x less than y$ and $y less than z. rightwards double arrow x less than z blank i. e. blank x blank R blank z$
Hence, $R$ is transitive

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