If $R = \{ (x,\,y)|x,\,y \in Z,\,{x^2} + {y^2} \le 4\} $ is a relation in $Z$, then domain of $R$ 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
- A
$\{0, 1, 2\}$
- B
$\{0, -1, -2\}$
- C
$\{-2, -1, 0, 1, 2\}$
- D
None of these
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Let $R$ be a reflexive relation on a finite set $A$ having $n$-elements, and let there be m ordered pairs in $R$. Then
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A relation on the set $A\, = \,\{ x\,:\,\left| x \right|\, < \,3,\,x\, \in Z\} ,$ where $Z$ is the set of integers is defined by $R= \{(x, y) : y = \left| x \right|, x \ne - 1\}$. Then the number of elements in the power set of $R$ is
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- [JEE MAIN 2014]
The void relation on a set $A$ is
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If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is
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Show that the relation $\mathrm{R}$ in the set $\mathrm{A}$ of points in a plane given by $\mathrm{R} =\{( \mathrm{P} ,\, \mathrm{Q} ):$ distance of the point $\mathrm{P}$ from the origin is same as the distance of the point $\mathrm{Q}$ from the origin $\}$, is an equivalence relation. Further, show that the set of all points related to a point $\mathrm{P} \neq(0,\,0)$ is the circle passing through $\mathrm{P}$ with origin as centre.
Show that the relation $\mathrm{R}$ in the set $\mathrm{A}$ of points in a plane given by $\mathrm{R} =\{( \mathrm{P} ,\, \mathrm{Q} ):$ distance of the point $\mathrm{P}$ from the origin is same as the distance of the point $\mathrm{Q}$ from the origin $\}$, is an equivalence relation. Further, show that the set of all points related to a point $\mathrm{P} \neq(0,\,0)$ is the circle passing through $\mathrm{P}$ with origin as centre.