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

Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R =\{( a , b ) \in A$ $\times A : b =| a |$ or $\left.b ^2= a +1\right\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is $........$.

If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12,6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$ , then relation $R$ is

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 $A =\{2,3,4\}$ and $B =\{8,9,12\}$. Then the number of elements in the relation $R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right.$ divides $b_2$ and $a_2$ divides $\left.b_1\right\}$ is:

Let $R$ be a relation on $N \times N$ defined by $(a, b) R$ (c, d) if and only if $a d(b-c)=b c(a-d)$. Then $R$ is