set theory

Question

whether true or false?

If a relation R on set A is irreflexive and transitive then R is antisymmetric.

I am getting false but answer is true..can someone explain with examples

Answer 1

take set A={ 1,2,3}  aRb iff a<b

so define on this relation a set

v={(1,2),( 2,3 ),(1,3) }

so the above set v is ir reflexive and transitive now to check this set is ATS or not

ATS  : (a<b)&(b<a) --------> a= b

CLEARLY LHS of the above implication is false so the above implication become true .  so statement is true ! if u find mistake than let me know .

Comments

Hey,

set R = {(1,2)(2,1)} is not transitive.

For it to be transitive you will have to add  {(1,1),(2,2)} to R.

According to me, the given statement is TRUE.

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ya...I think u r ryt..thanks:)
this was the point i was missing
we can have a=c while doing (a,b) and (b,c)
i was taking only distinct values

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Sorry guys. I gave wrong definition of irreflexive relation.