917 views
0 votes
0 votes

A relation R on a set of positive integers is defined by (a,b) belongs to R iff a and b are relatively prime.

Which of the following is true about R?

a. Symmetric and Reflexive

b. Symmetric and irreflexive

c.Symmetric and transitive

d. Symmetric and  not transitive

 

The Ans is given as (d) but I think (b) is true. Any thoughts?

1 Answer

0 votes
0 votes

Relation - is relatively prime.

Check Reflexive property:

aRa is not relatively prime . Hence not reflexive

Check Irreflexive property:

aRa

Ex. (4,8) is not relatively prime. Hence not Irreflexive

Check Symmetric property:

aRb => bRa

(3,4) is relatively prime and (4,3) also relatively prime. Hence Symmetric.

Check Transitive property:
aRb &bRc then aRc

Proof by Counter Example:

Ex:

(3,5) is relatively prime

(5,6) is relatively prime

but (3,6) is not relatively prime

Hence not transitive.

So option D is correct.

Related questions

0 votes
0 votes
1 answer
1
srestha asked May 15, 2018
1,150 views
How to distinguish between countably finite , countably infinite , uncountably infinite set?for reference see this ques:https://gateoverflow.in/36654/why-set-of-all-funct...
2 votes
2 votes
1 answer
3
ram_18051996 asked Jun 15, 2017
516 views
{ a } ∈ A buta ∉ Awhy ?here ' a is the element of set {a} ' ,and ' set {a} is the element of A" , so " a also element of A " . please clear my doubt .