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Given $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$. Then the relation $R$ is called what?
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In a set $A$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$, then what is the relation $R$ called?
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Mar 8, 2013
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balaji.thirumalai
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ANSWER: A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$
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Mar 8, 2013
by
balaji.thirumalai
A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R$ and which of the following conditions must also hold true?
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In a set $A$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$, then what is the relation $R$ called?
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A relation $R$ in $X$ given by $R = X \times X$ is called what?
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