Test series

Question

R is a relation define on set A = {1,2,3}. The R is symmetric, transitive and irreflexive. Then |R| =

Comments

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Answer 1

Given that,

it is ir-reflexive ===> (x,x) not allowed.

it is symmetric and transitive ===> if (x,y) is in R, then (y,x) must be present in R.

But note that as per transitive if (x,y) and (y,x) is present in R, then (x,x) must be in R, but we can't have such pairs due to ir-reflexive.

∴ R can be only EMPTY SET ===> |R| = 0

Comments

if R ={Ф} ,  then |R| = 1  ???

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R is empty set which means there is nothing then |R| will be zero not 1

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check i have edited

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R{$\Phi$} means R{{}} then yes |R| =1

But here R is empty set means R={} so |R|=0

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@ Prateek Raghuvanshi

maximum cardinality will be (n²−n) means 6.right??

why ? can you give any example ?

 

@nephron

in this question, it is R = Φ ===> |R|=0

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You mean we have a null relation.

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@Shaik Masthan, sorry brother only empty set will be the answer.thank you

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@nephron

yes

 

@Prateek Raghuvanshi

ok brother