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Question

# Let A={p,q,r}. Which of the following is an equivalence relation in A?

A
R1={(p,q),(q,r),(p,r),(p,p)}
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B
R2={(r,q),(r,p),(r,r),(q,q)}
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C
R3={(p,p),(q,q),(r,r),(p,q)}
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D
None of these
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Solution

## The correct option is D None of theseGiven A={p,q,r}R1={(p,q),(q,r),(p,r),(p,p)}R1 is not reflexive as it does not have (q,q),(r,r) . So, R1 is not an equivalence relation on A. R2={(r,q),(r,p),(r,r),(q,q)}R2 is not reflexive as it does not have (p,p) . So, R2 is not an equivalence relation on A. R3={(p,p),(q,q),(r,r),(p,q)}R3 is reflexive but not symmetric as (p,q) is there ,but not (q,p)

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