[b]Let [math]g\left(P,Q\right)=[/math][math]g\left(P,Q\right)=max\left(x_P,x_Q\right)+max\left(y_P,y_Q\right)[/math]. [br][br]a)[/b] We can show that [math]g\left(P,Q\right)[/math] is not a metric. Consider the points [math]P=\left(-2,0\right)[/math] and [math]Q=\left(-1,-1\right)[/math]. Then, [math]g\left(P,Q\right)=max\left(-2,-1\right)+max\left(0,-1\right)=-1+0=-1.[/math] This contradicts the first metric axiom, thus [math]g\left(P,Q\right)[/math] is not a metric. [br][b]b) [/b]does not apply [br][b]c) [/b]Does not apply