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+5 votes

The less-than relation, <, on reals is

  1. a partial ordering since it is asymmetric and reflexive

  2. a partial ordering since it is antisymmetric and reflexive

  3. not a partial ordering because it is not asymmetric and not reflexive

  4. not a partial ordering because it is not antisymmetric and reflexive

  5. none of the above

asked in Set Theory & Algebra by Veteran (58.9k points)   | 292 views

2 Answers

+8 votes
Best answer
relation less than is :
a. not Reflexive
b. Irreflexivew
b. not symmetric
c. Asymmetric
d. Anti symmetric

relation is not POSET because it is irreflexive.
check AntiSymmetry..
aRb != bRa unless a=b.

A relation may be 'not Asymmetric and not reflexive' bt still Antisymmetric.
as {(1,1) (1,2)}

not Asymmetric and Irreflexive = Antisymmetric
Option E
answered by Veteran (45.9k points)  
selected by
given relation is not Poset and reason it it is not reflexive..
it has nothing to do with asymmetry.
+1 vote

Since  "<" relation neither reflexive nor patialy ordering on set of real number.

But it is anti Symmetric relation.Therefor Option E will be appropriate option for it.

answered by Loyal (4.7k points)  
Can you explain how it is anti symmeteric?

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