why isnt {(a,a)} reflexive on a R= {(a,b,c)}......and is {(b,c)} in a relation R={(a,b,c)} is symetric transitive or reflexive....

Asked by Farooq Ahmad Shah | 19th Dec, 2015, 07:49: AM

Expert Answer:

O u r space r e s p o n s e space t o space y o u r space p r e v i o u s space q u e s t i o n colon
 
 
L e t space A equals open curly brackets a comma b comma c close curly brackets space b e space a space s e t. L e t space R space b e space a space r e l a t i o n space o n space a space s e t space A space s u c h space t h a t space R equals open curly brackets open parentheses a comma a close parentheses close curly brackets A space r e l a t i o n space R space o n space a space s e t space A space i s space s a i d space t o space b e space a space s y m m e t r i c space r e l a t i o n space i f f space open parentheses a comma b close parentheses element of R space rightwards double arrow open parentheses b comma a close parentheses element of R G i v e n space t h a t space open parentheses a comma bold italic a close parentheses element of R T h u s comma space open parentheses a comma bold italic a close parentheses space i s space s a m e space a s space open parentheses bold italic a comma a close parentheses rightwards double arrow R space i s space s y m m e t r i c.  A space r e l a t i o n space o n space a space s e t space A space i s space s a i d space t o space b e space t r a n s i t i v e space r e l a t i o n space i f f space open parentheses a comma b close parentheses element of R comma space open parentheses b comma c close parentheses element of R space rightwards double arrow open parentheses a comma c close parentheses element of R space f o r space a l l space a comma b space a n d space c element of A. H e r e comma space open parentheses a comma bold italic a close parentheses element of R space a n d space space open parentheses bold italic a comma a close parentheses element of R rightwards double arrow open parentheses a comma a close parentheses element of R comma space w h i c h space i s space t r u e. rightwards double arrow R space i s space t r a n s i t i v e
R e s p o n s e space t o space y o u r space c u r r e n t space q u e r y colon I t space d e p e n d s space o n space t h e space d e f i n i t i o n space o f space t h e space s e t space A I f space A equals open curly brackets a close curly brackets space a n d space R equals open curly brackets open parentheses a comma a close parentheses close curly brackets comma space t h e n space R space i s space r e f l e x i v e.  I f space A equals open curly brackets a comma b comma c close curly brackets space a n d space R equals open curly brackets open parentheses a comma a close parentheses close curly brackets comma space t h e n space R space i s space n o t space r e f l e x i v e.  A space r e l a t i o n space o n space a space s e t space A space i s space s a i d space t o space b e space r e f l e x i v e space i f space e v e r y space e l e m e n t space o f space A space i s space r e l a t e d space t o space i t s e l f.  T h u s comma space R space i s space r e f l e x i v e space left right double arrow space open parentheses a comma a close parentheses element of R space f o r space a l l space a element of A.  E x a m p l e colon L e t space A equals open curly brackets 1 comma 2 comma 3 close curly brackets space a n d space R equals open curly brackets open parentheses 1 comma 1 comma close parentheses comma open parentheses 2 comma 2 close parentheses comma open parentheses 2 comma 1 close parentheses comma open parentheses 1 comma 3 close parentheses close curly brackets space i s space n o t space r e f l e x i v e comma space b e c a u s e comma space open parentheses 3 comma 3 close parentheses not an element of R  E x a m p l e colon L e t space A equals open curly brackets 1 comma 2 comma 3 close curly brackets space a n d space R equals open curly brackets open parentheses 1 comma 1 comma close parentheses comma open parentheses 2 comma 2 close parentheses comma space open parentheses 3 comma 3 close parentheses comma open parentheses 2 comma 1 close parentheses comma open parentheses 1 comma 3 close parentheses close curly brackets space i s space r e f l e x i v e.

Answered by Vimala Ramamurthy | 19th Dec, 2015, 11:28: AM