Question

Let N+2 denote the natural numbers greater than or equal to 2. Let mRn if gcd(m, n) > 1. The binary relation R on N2 is

Answer 1

Answer:

a)  Reflexive, Symmetric, Not Transitive

Step-by-step explanation:

Given $a\in N+2$ we have that $a\ge 2$ and then $\gcd(a,a)=a\ge 2$ thus the binary relation is reflexive. To show that is symmetric note that for $a,b\in N+2$ we have $\gcd(a,b)=\gcd(b,a)$ which implies the symmetric. In fact, the relation is not transitive, for example note that $\gcd(7,7^2)=7$ and $\gcd(5^2,5)$ but $\gcd(7,5)=1$.