First slide

Relations XII

Question

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

Moderate

A

Reflexive
B

Symmetric
C

Transitive
D

Anti-symmetric

Solution

$P = \{(x, y) ∣ x^{2} + y^{2} = 1, x, y \in R\} O b v i o u s l y P i s n o t r e f l e x i v e, b e c a u s e (1, 1) i s n o t a n e l e m e n t o f R I f (x, y) i s a n e l e m e n t o f P t h e n (y, x) a l s o a n e l e m e n t o f P S o, P i s s y m m e t r i c (0, 1), (1, 0) a r e e l e m e n t s o f P b u t (0, 0) i s n o t a n e l e m e n t o f P S o t h a t t h e r e l a t i o n P i s n o t t r a n s i t i v e H e n c e, t h e r e l a t i o n P i s n o t r e f l e x i v e, s y m m e t r i c, n o t T r a n s i t i v e . T h e r e f o r e, t h e 2 n d o p t i o n i s c o r r e c t$

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