Answer to Question #209913 in Discrete Mathematics for Sach

Question

A relation R on a set S is called asymmetric if (a, b) is in R implies that (a, b) is not in R. Which of the

relations in Q. No. 5 is asymmetric?

Answer 1

In set theory, A relation R on a set A is called asymmetric if no (y,x) ∈ R when (x,y) ∈ R.

Or we can say, the relation R on a set A is asymmetric if and only if, (x,y) ∈ R ⟹ (y,x) ∉ R.

For example:

If R is a relation on set A = {12,6} then {12,6} ∈ R implies 12>6, but {6,12} ∉ R, since 6 is not greater than 12.

Note: Asymmetric is the opposite of symmetric but not equal to antisymmetric.