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Which of the following is true?

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Number of equivalence relations on vowels in English language is 50.

Brother among humans is symmetric relation

$R o S$ and $S o R$ are symmetric only when $R = S$ (for relations R & S)

if $R o S = S o R$ then $R o S$ and $S o R$ are symmetric (for relations R & S)

answer is D.

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Detailed Solution

$R o S$ is symmetric if ${(R o S)}^{- 1} = R o S$

But ${(R o S)}^{- 1} = S^{- 1} o R^{- 1} = S o R$

$∴ R o S$ is symmetric if $R o S = S o R .$

Similarly $S o R$ is symmetric if $S o R = R o S$

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