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12th Class Mathematics Relations and Functions Question Bank Case Based (MCQs) - Relations and Functions

  • question_answer
    Directions : (16 - 20)
    Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line \[y=x-4\]. Let L be the set of all lines which are parallel on the ground and R be a relation on L.
    Answer the following using the above information.
    Let relation R be defined by \[R=\left\{ \left( {{L}_{1}},\,{{L}_{2}} \right) \right.\,:\,{{L}_{1}}\,|\,\,|\,\,{{L}_{2}}\] where \[\left. {{L}_{1}},\,{{L}_{2}}\,\in L \right\}\] then R is ............ relation

    A) Equivalence

    B) Only reflexive

    C) Not reflexive

    D) Symmetric but not transitive

    Correct Answer: A

    Solution :

    \[{{L}_{1}}\,|\,|\,\,{{L}_{1}}\,\,\Rightarrow R\] is reflexive \[{{L}_{1}}\,|\,|\,{{L}_{2}}\,\,\in \,\,R\,\,\Rightarrow {{L}_{2}}\,|\,\,|\,\,{{L}_{1}}\] \[\Rightarrow R\] is symmetric \[{{L}_{1}}\,|\,\,|\,\,{{L}_{2}}\,\,\in \,\,R,\,\,{{L}_{2}}\,\,|\,\,|\,\,{{L}_{3}}\,\in \,\,R\,\,\Rightarrow {{L}_{1}}\,|\,\,|\,\,{{L}_{3}}\,\,\in \,R\] \[\Rightarrow R\] is transitive \[\Rightarrow R\] is an equivalence relation.


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