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Question

The relation $R equals left curly bracket open parentheses 11 close parentheses comma open parentheses 22 close parentheses comma open parentheses 33 close parentheses comma open parentheses 12 close parentheses comma open parentheses 23 close parentheses comma left parenthesis 13 right parenthesis right curly bracket$ on set $A equals left curly bracket 12 comma 3 right curly bracket$ is

Reflexive but not symmetric
Reflexive but not transitive
Symmetric and transitive
Neither symmetric nor transitive

The correct answer is: Reflexive but not symmetric

Since $open parentheses 11 close parentheses comma open parentheses 22 close parentheses comma open parentheses 33 close parentheses element of R.$ Therefore, $R$ is reflexive. We observe that $left parenthesis 12 right parenthesis element of R$ but $open parentheses 21 close parentheses not an element of R comma$ therefore $R$ is not symmetric.
It can be easily seen that $R$ is transitive

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