Prove these parts of Theorem 2.6.10 as follows: (a) Prove part (b) using a combinat...

Prove these parts of Theorem 2.6.10 as follows:

(a) Prove part (b) using a combinatorial argument.

(b) Prove part (c) using a combinatorial argument.

(c) Prove part (c) algebraically.

(d) Use part (c) to prove part (a) of Theorem 2.6.10 by induction.