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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

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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 .

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