Consider the relation $R$ on the set $\{-2,-1,0,1,2\}$ defined by $(a, b) \in R$ if and only if $1+a b>0$. Then, among the statements :
I. The number of elements in R is 17
II. R is an equivalence relation
Let $R$ be a relation defined on the set $\{1,2,3,4\} \times\{1,2,3,4\}$ by
$$ \mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\} . $$
Then the number of elements in R is
Consider two sets $\mathrm{A}=\{x \in \mathrm{Z}:|(|x-3|-3)| \leq 1\}$ and
$\mathrm{B}=\left\{x \in \mathbb{R}-\{1,2\}: \frac{(x-2)(x-4)}{x-1} \log _e(|x-2|)=0\right\}$. Then the number of
onto functions $f: \mathrm{A} \rightarrow \mathrm{B}$ is equal to :
Let $\mathrm{A}=\{0,1,2, \ldots, 9\}$. Let R be a relation on A defined by $(x, y) \in \mathrm{R}$ if and only if $|x-y|$ is a multiple of 3.
Given below are two statements :
Statement I : $n(\mathrm{R})=36$.
Statement II : R is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below :
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