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sunainagupta

  • 2 years 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
    • 2 years ago
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    Reflexive means: \[ \forall x \quad xRx \]

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

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

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

  5. wio
    • 2 years ago
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    @sunainagupta Are you following?

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

  7. wio
    • 2 years 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
    • 2 years ago
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    thank you!

  9. sunainagupta
    • 2 years 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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