Let R be the relation defined on the set of natural numberN as aRb; a, b ∈ N, if a divides b.Then, which one of the following is correct?a)R is reflexive onlyb)R is symmetric onlyc)R is transitive onlyd)R is reflexive and transitiveCorrect answer is option 'D'. Can you explain this answer?

Question

Let R be the relation defined on the set of natural numberN as aRb; a, b &isin; N, if a divides b.Then, which one of the following is correct?a)R is reflexive onlyb)R is symmetric onlyc)R is transitive onlyd)R is reflexive and transitiveCorrect answer is option 'D'. Can you explain this answer?

Answer

Unfortunately, the second part of your question is missing. Could you please provide the complete definition of the relation R?

Answer

For reflexive _aR_a implies a divides a
So, R is reflexive.
For symmetric
_aR_b impliesa divides b
_bR_a impliesa divides a
which may not be possible.
So, R is not symmetric.
For transitive
_aR_b impliesa divides b implies b = ka _bR_c impliesb divides c implies c = lb Now, c = Ika
or a divides c implies aRc
or _bR_c implies _cR_a
Thus, R is transitive.

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