The relation R in the set z of integer given by R = {(a,b) : a-b is divisible by 5} is
(a) reflexive
(b) reflexive but not symmetric
(c) symmetric and transitive
(d) an equivalence relation
# please explain the reflexive part .
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d)equivalent relation
reflexive : a - a = o
=) a - a = 0.5
=) a - a is divisible by 5
=) ( a,a ) (- R
so it is reflexive .
reflexive : a - a = o
=) a - a = 0.5
=) a - a is divisible by 5
=) ( a,a ) (- R
so it is reflexive .
Nastymath:
can you explain with another example please?
that is a ideal solution .. ok another example. let a = 7 we need to prove that ( a,a ) (- R .. now 7 =7 =) 7 - 7 = 0. =) 7 - 7 = 0.5. =) 7 - 7 is divisible by 5 so ( 7,7 ) (- R so R is reflexive
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