Let P = {(x,y) x 2 + y 2 = 1 , x , y ∈ R } . Then P is. Options: A . &nbsp Reflexive B . &nbsp Symmetric C . &nbsp Transitive D . &nbsp Anti-symmetric

Let P = {(x,y) x2+y2=1,x,y∈R}. Then P is.

Question -

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

Options:

A . Reflexive

B . Symmetric

C . Transitive

D . Anti-symmetric

Answer: Option B
:
B

Here we can see that the relation is neither reflexive nor transitive but it is symmetric,

because $x^{2} + y^{2} = 1 \Rightarrow y^{2} + x^{2} = 1$

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