Answer:
a) Reflexive, Symmetric, Not Transitive
Step-by-step explanation:
Given [tex]a\in N+2[/tex] we have that [tex]a\ge 2[/tex] and then [tex]\gcd(a,a)=a\ge 2[/tex] thus the binary relation is reflexive. To show that is symmetric note that for [tex]a,b\in N+2[/tex] we have [tex]\gcd(a,b)=\gcd(b,a)[/tex] which implies the symmetric. In fact, the relation is not transitive, for example note that [tex]\gcd(7,7^2)=7[/tex] and [tex]\gcd(5^2,5)[/tex] but [tex]\gcd(7,5)=1<2[/tex].
