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sunainagupta

  • one year ago

Consider a set X = [2, 3, 4) and the Relation defined on X by. R = {(2, 2) (2, 3) (3, 3) (3, 4) (2, 4) (4, 4)}. Find whether R is : i) Reflexive ii) Symmetric iii) Transitive Also justify your answer.

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  1. wio
    • one year ago
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    Reflexive means: \[ \forall x \quad xRx \]

  2. wio
    • one year ago
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    It's reflexive since it contains \((2,2)\), \((3,3)\), and \((4,4)\).

  3. wio
    • one year ago
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    Symmetric means: \[ \forall x\quad xRy\iff yRx \]

  4. wio
    • one year ago
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    It's not symmetric because it contains \((2,3)\) but not \((3,2)\).

  5. wio
    • one year ago
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    @sunainagupta Are you following?

  6. wio
    • one year ago
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    Transitive means: \[ \forall x\quad xRy\wedge yRz\implies xRz \]

  7. wio
    • one year ago
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    Let me rehash, since my notation was strange before. Reflexive \[ \forall x \quad (x,x)\in \mathcal{R} \] Symmetric \[ \forall x,y \quad (x,y)\in \mathcal{R} \iff (y,x)\in \mathcal{R} \] Transitive \[ \forall x,y,z \quad (x,y)\in \mathcal{R} \wedge (y,z)\in \mathcal{R} \implies (x,z)\in \mathcal{R} \]

  8. sunainagupta
    • one year ago
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    thank you!

  9. sunainagupta
    • one year ago
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    A survey among the students of college. 60 Study Hindi, 40 study Spanish, and 45 study Japanese, Further 20 study Hindi and Spanish, 25 study Hindi and Japanese, 15 study Spanish and Japanese and 8 study all the languages. Find the followings: i) How many students are studying at least one language? ii) How many students are studying only Hindi ? iii) How many students are studying only Japanese ?

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