- Home
- Standard 12
- Mathematics
1.Relation and Function
normal
Let $r$ be a relation from $R$ (Set of real number) to $R$ defined by $r$ = $\left\{ {\left( {x,y} \right)\,|\,x,\,y\, \in \,R} \right.$ and $xy$ is an irrational number $\}$ , then relation $r$ is
A
reflexive and symmetric only
B
symmetric only
C
symmetric and transitive only
D
equivalence relation
Solution
Reflexive : $a^{2}=$ irrational number
$\Rightarrow$ It is not true for all real numbers
Symmetric:
If $a b=$ irrational number, then
$ba$ = irrational number
$\therefore$ $r$ is symmetric relation
Transistive:
$(1, \sqrt{2}) \in \mathrm{r}$
$(\sqrt{2}, 2) \in \mathrm{r}$
but $(1,2) \notin \mathrm{r}$
$\therefore$ It is not transistive
Standard 12
Mathematics
