Sir 
 If any set have only two element then how to explain transitive relation.
 
 If x is wife of y then it is a transitive relation
 
Plz also explain antisymmeric relation by example

Asked by roshan dongre | 22nd Jun, 2014, 02:49: PM

Expert Answer:

N o w space c o n s i d e r space t h e space s e t space h a v i n g space e l e m e n t s space left parenthesis 1 comma 1 right parenthesis space a n d space a s s u m e space t h e space r e l a t i o n space a s space x squared T h u s comma space 1 R 1 comma space 1 R 1 rightwards double arrow 1 R 1 A n d space h e n c e space t h e space r e l a t i o n space i s space t r a n s i t i v e. x space i s space w i f e space o f space y space i s space n o t space a space t r a n s i t i v e space r e l a t i o n space b e c a u s e space a space p e r s o n space c a n n o t space b e space a space m a l e space a n d space a space f e m a l e space a t space t h e space s a m e space t i m e. A space b i n a r y space r e l a t i o n space R space o n space a space s e t space X space i s space a n t i s y m m e t r i c e space i f space t h e r e space i s space n o space p a i r space o f space d i s t i n c t space e l e m e n t s space o f space X space e a c h space o f w h i c h space i s space r e l a t e d space b y space R space o t space t h e space o t h e r. space T h a t space i s space R space o s space a m t i s y m m e t r i c space i f space a n d space o n l y space i f space f o r space a l l space a space a n d space b e space i n space X comma space i f space R left parenthesis a comma b right parenthesis space a n d space R left parenthesis b comma a right parenthesis comma space t h e n space a equals b E x a m p l e : I f space m space a n d space n space a r e space d i s t i n c t comma space a n d space m space i s space a space f a c t o r space o f space n comma t h e n space n space c a n n o t space b e space a space f a c t o r space o f space m.

Answered by Vimala Ramamurthy | 23rd Jun, 2014, 01:31: PM