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sunainagupta Group Title

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.

  • 11 months ago
  • 11 months ago

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  1. wio Group Title
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    Reflexive means: \[ \forall x \quad xRx \]

    • 11 months ago
  2. wio Group Title
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    It's reflexive since it contains \((2,2)\), \((3,3)\), and \((4,4)\).

    • 11 months ago
  3. wio Group Title
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    Symmetric means: \[ \forall x\quad xRy\iff yRx \]

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

    • 11 months ago
  5. wio Group Title
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    @sunainagupta Are you following?

    • 11 months ago
  6. wio Group Title
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    Transitive means: \[ \forall x\quad xRy\wedge yRz\implies xRz \]

    • 11 months ago
  7. wio Group Title
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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 \[ \forall x,y,z \quad (x,y)\in \mathcal{R} \wedge (y,z)\in \mathcal{R} \implies (x,z)\in \mathcal{R} \]

    • 11 months ago
  8. sunainagupta Group Title
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    thank you!

    • 11 months ago
  9. sunainagupta Group Title
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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 ?

    • 11 months ago
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