Here A={4,6,10,12}

so A*A={(4,4),(4,6),(4,10),(4,12),(6,4),(6,6),(6,10),(6,12),(10,4),(10,6),(10,10),(10,12),(12,4),(12,6),(12,10),(12,12)}

so the relation R # A*A

where # indicates subset

R={(x,y) s.t. x and y have only one common factor and (x,y) # A*A}

Find the Elements in A*A such that they have only one common factor.

We see that (4,6),(4,10),(6,4),(6,10),(10,4),(10,6),(10,12),(12,10) are the elements which have only one common factor EXCEPT 1

But Note that 1 IS ALSO A COMMON FACTOR, SO ALL THE ELEMENTS OF A*A HAS MORE THAN ONE COMMON FACTOR HENCE THE RELATION IS VOID SET.