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1. Given two functions f, g : R - R, we say . f is grander than g if ]r ER, s.t. Vy ER, x f(y) > g(y). . EDIT: f is worthier than g if Vr e R, By e R s.t. x g(y). We also need a new notation. Given t ( R and a function h : R - R, define h; : R - R by h,(x) = h(c) +t. Below are 3 claims. Which ones are true and which ones are false? If a claim is true. Prove it. If a claim is false, show it with a counterexample. (a) For all functions f, g : R - R, if f is grander than g, then f is worthier than g. (b) For all functions f, 9 : R - R, if f is worthier than g, then f is grander than g. (c) For all functions g : R - R, there exists a function f : R - R s.t. for any t E R, f is worthier than gt. Hint: First consider the case where g is defined by g(x) = 0