If Ris a relation on the set of natural

Question

If Ris a relation on the set of natural number such that aRb > a = 3k. b for some integer k, then Ris :-
O
Symmetric, transitive but not reflexive
Reflexive, symmetric but not transitive
Reflexive, transitive but not symmetric
An equivalence relation

Kunduz · Accepted Answer

solution -
i equivalence Relation :-
A Relation &R' is an equivalent relation
in set "Al if & only if
IR is reflexive ie for all aER (a, a) ER
ii) R is symmetric ie(a,b) ER Then Coal ER
iii) R in transitive i e caseR and (6,() ER
then a, c) ER
question,
Ris a relation on the set of natural No.
such that a Rb a = 3 k. b for some Integerk.
Ris reflexive ice Jackall a ER, (a,0) ER
a
When k=0
Ris symmetric i. e (a,b) El then (5,9) ER
Whenko
R is transitie ie (a,b) and (3,0) +R
Then (a, C) ER Whenko
It is equivalent Relation
option will se correct.
7
don

If Ris a relation on the set of natural number such that aRb > a = 3k. b for some integer k, then Ris :- O Symmetric, transitive