Relation and Functions

Question

Let R is a relation define on set A = {1,2,3,4,5}. The R is symmetric, transitive and irreflexive. Then |R| =

Comments

There is only one relation is possible in this case.

$R=\left \{ \right \}$

So,

$|R|=1$

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It should be 0, right?

As R does not contains any element.

Please correct me if I am wrong.

Answer 1

 R to be in symmetric, transitive and irreflexive then R={}, |R|=0

Comments

nephron just took a small example let A ={1,2,3}

now read question R shoulb be irreflexive so no (a,a) type pairs should be there .

now to be symmetric if (a,b) is there (b,a) should be there 

;let write all such pairs R={(1,2),(2,1),(1,3),(3,1) and so on...........}

now this R should be transitivw also  so is (1,2) and (2,1) is present then (1,1) shoulb be also present which is impossible due to irreflexive nature hence phi is only element.

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 eyeamgj

then |R|  should be 1

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yes