Question

Let R be the relation defined on the set of natural number N as aRb; a, b ∈ N, if a divides b. Then, which one of the following is correct? 

(a) R is reflexive only 

(b) R is symmetric only 

(c) R is transitive only 

(d) R is reflexive and transitive

Answer 1

Correct option is (c)

Explanation:

For reflexive 

aRa ⇒ a divides a 

∴ R is reflexive. 

For symmetric 

aRb ⇒  a divides b 

bRa ⇒ b divides a 

which may not be possible. 

∴ R is not symmetric. 

For transitive 

aRb ⇒ a divides b ⇒ b = ka 

bRc ⇒ b divides c ⇒ c = lb

Now, c = lka

⇒ a divides c ⇒ aRc ⇒ aRb, bRc ⇒ cRa

Thus, R is transitive