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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.
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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wio
 2 years ago
Best ResponseYou've already chosen the best response.1Reflexive means: \[ \forall x \quad xRx \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.1It's reflexive since it contains \((2,2)\), \((3,3)\), and \((4,4)\).

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Symmetric means: \[ \forall x\quad xRy\iff yRx \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.1It's not symmetric because it contains \((2,3)\) but not \((3,2)\).

wio
 2 years ago
Best ResponseYou've already chosen the best response.1@sunainagupta Are you following?

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Transitive means: \[ \forall x\quad xRy\wedge yRz\implies xRz \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Let 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 \[ \forall x,y,z \quad (x,y)\in \mathcal{R} \wedge (y,z)\in \mathcal{R} \implies (x,z)\in \mathcal{R} \]

sunainagupta
 2 years ago
Best ResponseYou've already chosen the best response.0A 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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