$2$ points$)$ Let d : U $\backslash$times U $[0,1]$ be any distance function mapping pairs of elements to adistance in the range $[0,1].$ Prove that, for there to exist a locality sensitive hash functionh with collision probability Pr$[$h$($x$)=$ h$($y$)]=1$d$($x$,$y$),$ then d must satisfy the triangleinequality. I.e$.,$ for all x$,$y$,$z we must have d$($x$,$z$)$ d$($x$,$y$)+$ d$($y$,$z$).$ Hint: Rewrited$($x$,$y$)=$ Pr$[$h$($x$)=$ h$($y$)].$