Question

Let $P=\left\{\right(x,y)|x^2+y^2=1,x,y\in R\}$. Then $P$ is

• A. a reflexive relation
• B. a symmetric relation
• C. a transitive relation
• D. an anti-symmetric relation

Answer 1

The correct option is B a symmetric relation

$\because (1,1),(0,0)\notin P$
$\therefore P$ is not reflexive as $(x,x)\notin P$

Now If $(x,y)\in P\Rightarrow x^2+y^2=1\Rightarrow y^2+x^2=1$
$\therefore (y,x)\in P$
Hence, $P$ is a symmetric relation

Also $(-\frac{3}{4},\frac{4}{5})\in P$ and $(\frac{4}{5},\frac{3}{4})\in P$
but $(-\frac{3}{4},\frac{3}{4})\notin P$

Hence $P$ is not transitive