Set Relation

Question

Answer please explain the ans.

R is antisymmetric then aRb, bRa -> a=b so a-b=0 and 0 is not odd positive then how it is antisymmetric?

Comments

@Dilip

According to the given relation you cannot take a=b because there is no element which is present in it with a=b like (1,1) , (2,2) are not in relation.

Try to find out the elements of relation then calculate further :)

Answer 1

no probs because ((3,2) (8,3}) akso making antisymmetric relation, and diagonal elements are not included hence not reflexive because 0 is not odd

Answer 2

Let's check for reflexive first

aRa = a-a = 0 which is not odd positive integer. So option b), c), d) gets eliminated because reflexive is necessary for these three options. d) is the answer clearly but let's see how? 

A relation is antisymmetric if aRb is in relation and if bRa is also in relation then a=b that means diagonal elements like (1,1), (2,2) etc can be present, it is not compulsory that they should be present. However elements like (3,2) , (5,2) if present then  (2,3) , (2,5) must not be present because a=b property voilates. 

So for the given relation If we try to find out the elements then it should be like..

R = { (2,1) , (5,2) , (6,1) ........etc} 

Clearly R is antisymmetric.

Option a) is correct answer