The relation $R$ defined on a set $A$ is antisymmetric if $(a,\,b) \in R \Rightarrow (b,\,a) \in R$ for

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \Leftrightarrow \alpha \bot \beta ,\,\alpha ,\,\beta \in L$. Then $R$ is

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $\mathrm{R}$ in the set $\mathrm{Z}$ of all integers defined as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{x}-\mathrm{y}$ is an integer $\}$

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a,\,b)|a \ge b,\,a,\,b \in R\} $. Then ${R_1}$ is

The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )$, (b, d) $\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is $………$