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Question
Discuss the following relation for reflexivity, symmetricity and transitivity:
The relation R defined on the set of all positive integers by “mRn if m divides n”
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Solution
S = {set of all positive integers}
(a) mRm ⇒ ‘m’ divides’m’ ⇒ reflexive
(b) mRn ⇒ m divides n but
nRm ⇒ n does not divide m
(i.e.,) mRn ≠ nRm
It is not symmetric
(c) mRn ⇒ nRr as n divides r
It is transitive
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