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Relations and Functions
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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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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Mar 8, 2013
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ANSWER: $(a_2,a_1)\in R$. A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
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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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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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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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True or False: An integer m is said to be related to another integer n if m is a integral multiple of n.This relation in Z is reflexive,symmetric and transitive.
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Fill in the blank: A relation R in a set A is called ______ relation, if each element of A is related to every element of A, i.e., R = A × A.
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