First slide

Relations XII

Question

$Let R be a relation on the set N of natural numbers denoted by n R m \Leftrightarrow n is a factor of m (i.e., n ∣ m) . Then, R is$

Moderate

A

Reflexive and symmetric
B

Transitive and symmetric
C

Equivalence
D

Reflexive, transitive but not symmetric.

Solution

Every natural number is factor to it self, so that R is reflexive
If (a,b) is an element of R, it means a is a factor of b, in this case b is not factor of a, so that (b,a) does not belongs to set R
so that the relation is not symmetric
Suppose that (a,b), (b,c) are elements of the relation R
it means a is factor of b and b is factor of c
it gives a is factor of c
Therefore, (a,c) is an element of R
It implies that the relation is transitive.
Hence, the relation is reflexive and transitive

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