Question

Let R be a relation between A and B. R is asymmetric if and only if ________

(a) Intersection of D(A) and R is empty, where D(A) represents diagonal of set

(b) R^-1 is a subset of R, where R^-1 represents inverse of R

(c) Intersection of R and R^-1 is D(A)

(d) D(A) is a subset of R, where D(A) represents diagonal of set

The question was asked by my school principal while I was bunking the class.

Asked question is from Types of Relations in section Relations of Discrete Mathematics

Answer 1

The correct choice is (a) Intersection of D(A) and R is empty, where D(A) represents diagonal of set

Easiest explanation: A relation is asymmetric if and only if it is both antisymmetric and irreflexive. As a consequence, a relation is transitive and asymmetric if and only if it is a strict partial order. If D(A) is a diagonal of A set and intersection of D(A) and R is empty, then R is asymmetric.