Let R be the relation defined on a set of natural numbers N as follows:

xRygcd(x+1,y+1)2.

Is R reflexive ?

Is R symmetric ?

Is R transitive ?

I am able to answer reflexivity and symmetry, but require assistance with transitivity.

For reflexivity, since xN,x+11,xRx(x+1,x+1)2, hence R is reflexive.

For symmetry, since gcd(x+1,y+1)=gcd(y+1,x+1)2 for some x,yN yRxgcd(y+1,x+1)2

For transitivity, let x,y,zNs.t.xRygcd(x+1,y+1)2andyRzgcd(y+1,z+1)2

How to proceed from this point onward ?

Please use latex, as images are difficult to interpret!