anonymous
  • anonymous
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.
Discrete Math
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Reflexive means: \[ \forall x \quad xRx \]
anonymous
  • anonymous
It's reflexive since it contains \((2,2)\), \((3,3)\), and \((4,4)\).
anonymous
  • anonymous
Symmetric means: \[ \forall x\quad xRy\iff yRx \]

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anonymous
  • anonymous
It's not symmetric because it contains \((2,3)\) but not \((3,2)\).
anonymous
  • anonymous
@sunainagupta Are you following?
anonymous
  • anonymous
Transitive means: \[ \forall x\quad xRy\wedge yRz\implies xRz \]
anonymous
  • anonymous
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 \[ \forall x,y,z \quad (x,y)\in \mathcal{R} \wedge (y,z)\in \mathcal{R} \implies (x,z)\in \mathcal{R} \]
anonymous
  • anonymous
thank you!
anonymous
  • anonymous
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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