Problem $7(10$ points$)$: Which of the following are admissible, given admissible heuristics h$1,$ h$2?$ Which of the following

are consistent, given consistent heuristics h$1,$ h$2?$ Justify your answer.

a$)$ h$($n$)=$ min$\{$h$1($n$),$ h$2($n$)\}$

b$)$ h$($n$)=$ wh$1($n$)+(1$ w$)$h$2($n$),$ where $0$ w $1$

c$)$ h$($n$)=$ max$\{$h$1($n$),$ h$2($n$)\}$