r is a relation on R defined by R={(a,b) / a=kb for some rational k}. Check if it is equivalence relation or not.
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no it is not equivalence relation for non zero a and b
reflexive. b=a
hence k=1 rational
symettric interchange a and b
hence b=ka k here is also rational
transitive if a=kb,b=kc then a=k^2 c
k^2 is rational
hence equivalence
if a or b=0 then not equivalent
hence answer is not equivalence
reflexive. b=a
hence k=1 rational
symettric interchange a and b
hence b=ka k here is also rational
transitive if a=kb,b=kc then a=k^2 c
k^2 is rational
hence equivalence
if a or b=0 then not equivalent
hence answer is not equivalence
Bargavee:
can you tell me why it is not symmetric?
you have only said 5,0 and 0,5 if interchange then k infinity is not a rational no
okay got it. thanks
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