A={1,2,3,4}, THEN R={(1,2),(1,3),(3,3),(3,1)} IS A __________ ans. NON SYMMETRIC RELATION ANTI SYMMETRIC RELATION REFLEXIVE RELATION TRANSITIVE RELATION

The given relation R={(1,2),(1,3),(3,3),(3,1)} on set A={1,2,3,4} can be analyzed as follows:

1. Non-Symmetric Relation: A relation is said to be non-symmetric if there exists (a,b) in R and (b,a) not in R for a ≠ b. Here, we have (1,2) in R but (2,1) is not in R. So, R is a Non-Symmetric Relation.

2. Anti-Symmetric Relation: A relation is said to be anti-symmetric if there exists (a,b) in R and (b,a) in R then a = b. Here, we have (3,3) in R and (3,3) in R with 3=3. But we also have (1,3) in R and (3,1) in R with 1 ≠ 3. So, R is not an Anti-Symmetric Relation.

3. Reflexive Relation: A relation is said to be reflexive if (a,a) is in R for every a in A. Here, (1,1), (2,2) and (4,4) are not in R. So, R is not a Reflexive Relation.

4. Transitive Relation: A relation is said to be transitive if whenever (a,b) and (b,c) are in R, then (a,c) is also in R. Here, (1,2) and (2,3) are in R but (1,3) is not in R. So, R is not a Transitive Relation.

Therefore, the given relation R is a Non-Symmetric Relation.