Which of the following are true and which are false? Explain your answers. 

a. Depth-first search always expands at least as many nodes as A^∗ search with an admissible heuristic.

b. h(n) = 0 is an admissible heuristic for the 8-puzzle.

c. A^∗ is of no use in robotics because percepts, states, and actions are continuous.

d. Breadth-first search is complete even if zero step costs are allowed.

e. Assume that a rook can move on a chessboard any number of squares in a straight line, vertically or horizontally, but cannot jump over other pieces. Manhattan distance is an admissible heuristic for the problem of moving the rook from square A to square B in the smallest number of moves.