Solution set of $x \equiv 3$ (mod $7$), $p \in Z,$ is given by

If $R$ is an equivalence relation on a set $A$, then ${R^{ - 1}}$ is

${x^2} = xy$ is a relation which is

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 $A =\{2,3,4,5, \ldots ., 30\}$ and $^{\prime} \simeq ^{\prime}$ be an equivalence relation on $A \times A ,$ defined by $(a, b) \simeq (c, d),$ if and only if $a d=b c .$ Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :

Let $R$ be a relation defined on $N$ as a $R$ b is $2 a+3 b$ is a multiple of $5, a, b \in N$. Then $R$ is