Consider a function $f: \mathbb{N} ightarrow \mathbb{N} $. Which of the following guarantees that " $f(n) \geq(2 n !$ for all integers $n \geq 2$ " can be proved by induction? (If $(E)$ is true you must select it rather than any other answer. If $(E)$ is false but $D$ is true, you must select (D) rather than (A) or (B).) Select one: (A): $f(2)=24$ and $f (k+1) \geq(2 k+2) ! f(k)$ for all integers $k \geq 2$ (B): $f(2)=30$ and $f(k+1) Igeq(2 k+2)(2 k+1) f(k)$ for all integers $k \geq 2$ (C): $f(2)=24$ and $f (k+1) \geq(2 k+2) f(k)$ for all integers $k \geq 2$ (D): both (A) and (B) (E): all of (A), (B) and (c) CS. SD. 133