CBSE Class 12-science Answered
Regarding Relations
Asked by thebluebloo | 31 Mar, 2009, 06:51: AM
Expert Answer
Let a, b c belong to Z
a is related to a , as a-a=0 is divisible by m(reflexive)
if a is related to b then b must be related to a as a is related to b implies a-b is divisible by m.So b-a must also be divisible by m
since
a-b=mk for some k in Z
then b-a=m(-k)
a-b=rm where r=-k belongs to Z
so ais related to b implies b is related to a((symmetric)
if a is related to b and b is related to c
then
a-b= mk(say, for some k in Z)
and
b-c= mp(say, for some p in Z)
So a-c=(a-b)+(b-c)=mk+mp=m(k+p) is divisible by m
thus a-c is divisible by m
i.e. a is congruent to c modulo m
i.e. a is related to c (transitive)
hence the answer.
Answered by | 31 Mar, 2009, 08:53: AM
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