The relation $R$ defined on a set $A$ is antisymmetric if $(a, b) \in R$ and $(b, a) \in R$ implies $a = b$ for all $a, b \in A$. Based on this definition,the relation $R$ is antisymmetric if $(a, b) \in R$ and $(b, a) \in R$ implies $a = b$,which is equivalent to saying that if $a \neq b$,then it is not possible for both $(a, b) \in R$ and $(b, a) \in R$ to be true. Therefore,the condition is that for $a \neq b$,we cannot have both $(a, b) \in R$ and $(b, a) \in R$.

  • A
    Every $(a, b) \in R$
  • B
    No $(a, b) \in R$
  • C
    No $(a, b) \in R$ such that $a \neq b$ and $(b, a) \in R$
  • D
    None of these

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