A 3 Prove the equation 2k=0 () = 2n for k, n € No

(a) using theorem 4.25 (binomial theorem)

(b) using theorem 4.24 (number of k-element subsets of a

n-element quantity)

(c) by means of complete induction according to n and lemma 4.23. (See here-

that the decomposition from lemma 4.23 only applies to 1 S k S n!)