$($d$)$ In order to apply $A^{**}$ search on the graph of Fig. $2,$ using A as the initial state and $E$ as the goal, we need an admissible heuristic function. Show that the function specified by the table below is admissible.

$[6$ marks$]$

$\backslash$table$[[$State$,$H$],[$A$,7],[$B$,6],[$C$,2],[$D$,1],[$E$,0]]$

Figure $2$: State$-$space graph and heuristic values for that graph.