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CBSE Class 12-science Answered

NCERT
Math- class 12
EX1.1
 
Qno.9 ii
A={x belongs to Z : 0<=x<=12}
R={(a,b):a=b}
 
i think
 
R={(0,0),(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8),(9,9),(10,10),(11,11),(12,12)}
then for transitive
(a,b) belong to R
(b,c) belong to R
(a,c) belong to R
R is transitive ???????????
 
suppose (0,0),(0,0) then  we say (0,0)=> transitive
 
 
please help and remove confusion
Asked by piyush_103_kumar | 10 Apr, 2016, 05:08: AM
answered-by-expert Expert Answer
G i v e n space r e l a t i o n space i s space straight R space equals space open curly brackets open parentheses straight a comma space straight b close parentheses colon space straight a space equals space straight b close curly brackets space. S o space a l l space t h e space e l e m e n t s space o f space t h e space r e l a t i o n space straight R space a r e space o f space t h e space t y p e space left parenthesis straight a comma space straight b right parenthesis space s u c h space t h a t space straight a space equals space straight b. L e t space left parenthesis straight a comma space straight b right parenthesis element of space straight R space a n d space space space left parenthesis straight b comma space straight c right parenthesis element of space straight R. t h e n space straight a space equals space straight b space a n d space straight b space equals straight c space rightwards double arrow space straight a equals space straight c rightwards double arrow space left parenthesis straight a comma space straight b right parenthesis element of space straight R space h e n c e space straight r space i s space t r a n s i t i v e. N o w space t a k e space straight a space equals space 0 space a n d space straight b space equals space 0 space a n d space straight c space equals space 0 left parenthesis straight a comma space straight b right parenthesis space equals space left parenthesis 0 comma space 0 right parenthesis space element of straight R space space a s space 0 space equals space 0 left parenthesis straight b space comma space straight c right parenthesis space equals space left parenthesis 0 space comma space 0 right parenthesis space element of space straight R space space space a s space 0 space equals space 0 left parenthesis straight a comma space straight c right parenthesis space equals space left parenthesis 0 comma space 0 right parenthesis space element of space straight R space space space a s space 0 space equals space 0 H e n c e space w e space c a n space s a y space t h a t space left parenthesis 0 comma 0 right parenthesis element of straight R comma space space left parenthesis 0 comma 0 right parenthesis element of straight R space t h e n space space w e space s a y space left parenthesis 0 comma 0 right parenthesis space element of straight R equals greater than space straight R space i s space t r a n s i t i v e.
 
Answered by Vijaykumar Wani | 11 Apr, 2016, 10:57: AM

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