SOLUTION: Relation R on the set of positive integers is defined by the rule that aRb means gcd(a, b) = 1. Is R reflexive? Symmetric? Transitive?

SOLUTION: Relation R on the set of positive integers is defined by the rule that aRb means gcd(a, b) = 1. Is R reflexive? Symmetric? Transitive?

Algebra.Com

Question 1030237: Relation R on the set of positive integers is defined by the rule that aRb means gcd(a, b) = 1. Is R reflexive? Symmetric? Transitive?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
R is symmetric, as aRb = bRa = 1. (Obviously.)
R is not reflexive, as 3R3 = 3.
R is not transitive, as 3R7 = 1 and 7R15 = 1, but 3R15 = 3.

RELATED QUESTIONS
Relation R on the set of positive integers is defined by the rule that aRb means gcd(a,... (answered by robertb)

Let P be the set of all triangles in a plane and R be the relation defined on P as aRb... (answered by ikleyn)

Let R be the relation on N defined by the rule that xRy means x + y is not divisible by... (answered by robertb)

Dear Tutor, please help me. Let A = {(1,2), (2,4), (3,6), (1,4), (2,8), (3,12),... (answered by ikleyn)

Can you help me solving this Q , I have problem with understand it Let A be the set... (answered by mathmate)

Determine if relation are reflexive, symmetric, anti-symmetric, transitive? relation R... (answered by lynnlo)

Let A = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, (answered by Jk22)

The relation ⋆ is defined on the set N by x⋆y if and only if every divisor of x is... (answered by ikleyn)

Let R be a relation on A={1,2,3,4} such that aRb means eans | a − b | ≤ 1. Find the... (answered by ikleyn)