Prove that f(n=O(g(n)) if and only if g(n)=12(f(n)). (2 pts) Tips/background: Math theorems often state that "a statement A holds if and only if a statement B holds" or, equivalently, "for A to hold, it is necessary and sufficient that B holds. These two formulations are equivalent, and to prove them, one needs to prove that (a) if B holds then A holds (which proves the "it" part), and also (b) if A holds then B holds (which proves the "only if" part). Note that from the statement "if A holds then B holds it does follow that "A holds only if B holds. To see this, assume the contrary, i.e., that "if A holds then B holds is true but "A holds only if B holds" is not. The latter would mean that B may not hold but A does hold. But this contradicts the first statement, i.e., that if A holds then B holds