Question

check whether the relation R in the set N of natural number given byR= (a, b) : a is divisor of b ? find is reflexive, symmetric, transitive. also whether the equivalence relations​

Answer 1

Answer:

If R is a relation on set N, then for it to be reflexive,

(a,a)∈R for all a∈N. But (4,4)∈

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R. Hence not reflexive.

If greatest common divisor of a and b is 2,

then greatest common divisor of b and a is also 2.

So, the given relation is symmetric. (∵aRb⇒bRa).

The given relation is not transitive as (6,10)∈R and (10,18)∈R, but (6,18)∈

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R (greatest common divisor of 6 and 18 is 6)