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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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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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Mar 8, 2013
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balaji.thirumalai
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ANSWER: $\;(a_1,a_3)\in R$. 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
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balaji.thirumalai
For a relation R in a set A to be called $\mathbf{symmetric}$, if $(a_1,a_2) \in R$, which of the following must also be true
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For a relation R in a set A to be called $\mathbf{symmetric}$, if $(a_1,a_2) \in R$, which of the following must also be true
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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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True or False: Every relation which is symmetric and transitive is also reflexive.
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If $(a,a) \in R\;$ for every $\; a\in\;A$, then what is the relation $R$ in the set $A$ is called?
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