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  • The number of the relations, on the set {1, 2, 3} containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is _______.Option: 1

The number of the relations, on the set {1, 2, 3} containing (1, 2) and (2, 3), which are reflexive and transitive
but not symmetric, is _______.

Option: 1

3


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} &A=\{1,2,3\}\\ &\text{For Reflexive }(1,1)(2,2),(3,3) \in \mathrm{R}\\ &\text{For transitive} : (1,2) \text{ and } (2,3) \in R \Rightarrow(1,3) \in R\\ &\text{Not symmetric }: (2,1) \text{ and } (3,2) \notin \mathrm{R}\\ & R_1=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\} \\ & R_2=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)(2,1)\} \\ & R_3=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)(2,1)\} \end{aligned}

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