how is {(a,a)} symmetric and transitive .......R={(a,b,c)}

Asked by Farooq Ahmad Shah | 17th Dec, 2015, 08:26: AM

Expert Answer:

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

Answered by Vimala Ramamurthy | 17th Dec, 2015, 10:47: AM