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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.
 7 months ago
 7 months 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.
 7 months ago
 7 months ago

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wioBest ResponseYou've already chosen the best response.1
Reflexive means: \[ \forall x \quad xRx \]
 7 months ago

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

wioBest ResponseYou've already chosen the best response.1
Symmetric means: \[ \forall x\quad xRy\iff yRx \]
 7 months ago

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

wioBest ResponseYou've already chosen the best response.1
@sunainagupta Are you following?
 7 months ago

wioBest ResponseYou've already chosen the best response.1
Transitive means: \[ \forall x\quad xRy\wedge yRz\implies xRz \]
 7 months ago

wioBest ResponseYou've already chosen the best response.1
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 \[ \forall x,y,z \quad (x,y)\in \mathcal{R} \wedge (y,z)\in \mathcal{R} \implies (x,z)\in \mathcal{R} \]
 7 months ago

sunainaguptaBest ResponseYou've already chosen the best response.0
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 ?
 7 months ago
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