Question

Let R be a relation on the set N of natural numbers defined by aRb if a divides b. Then R : 1) Reflexive and Symmetric e) Equivalence (b) Transitive and Symmetric (d) Reflexive, Transitive and not Symmetric​

Answer 1

Answer:

a) reflection

b translation

c symmetric

Step-by-step explanation:

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Answer 2

Answer

Correct option is

D

Reflexive, transitive but not symmetric

Let there be a natural number n,

We know that n divides n, which implies nRn.

So, Every natural number is related to itself in relation R.

Thus relation R is reflexive .

Let there be three natural numbers a,b,c and let aRb,bRc

aRb implies a divides b and bRc implies b divides c, which combinedly implies that a divides c i.e. aRc.

So, Relation R is also transitive .

Let there be two natural numbers a,b and let aRb,

aRb implies a divides b but it can't be assured that b necessarily divides a.

For ex, 2R4 as 2 divides 4 but 4 does not divide 2 .

Thus Relation R is not symmetric .