In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$
Is reflexive
Is symmetric
Is transitive
Possesses all the above three properties
Let $L$ be the set of all lines in $XY$ plane and $R$ be the relation in $L$ defined as $R =\{\left( L _{1}, L _{2}\right): L _{1} $ is parallel to $L _{2}\} .$ Show that $R$ is an equivalence relation. Find the set of all lines related to the line $y=2 x+4$
Let $A=\{1,2,3\} .$ Then number of equivalence relations containing $(1,2)$ is
If $R = \{ (x,\,y)|x,\,y \in Z,\,{x^2} + {y^2} \le 4\} $ is a relation in $Z$, then domain of $R$ is
Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is
Let $I$ be the set of positve integers. $R$ is a relation on the set $I$ given by $R =\left\{ {\left( {a,b} \right) \in I \times I\,|\,\,{{\log }_2}\left( {\frac{a}{b}} \right)} \right.$ is a non-negative integer$\}$, then $R$ is