1. True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample. (a) True or False: If x + c, then |x – c| is strictly greater than zero. (b) True or False: If |x- c| is strictly greater than zero, then x+ c. (c) True or False: x is a solution of 0 < |x – c| < 8 if and onlv if c – 8 < x < c+ 8. (d) True or False: If 0 < ]x – c| < 8, then x e (c – 8, c) U (c, c+ 8). (e) True or False: If | f (x)–L| < €, then L-e < f(x) < L+e. (f) True or False: If f(x) e (L – €, L + e), then 0 < f(x) < |L+ €|. (g) True or False: The fact that 0 < ]x – 3| < 0.25 guarantees that |(2x – 1) – 5| < 0.5 proves that lim (2x – 1) = 5. x+3 (h) True or False: lim(2x – 1) = 5 means that for all 8 > 0 there is some e > 0 such that if 0 < |x – c| < 8, then |(2x – 1) – 5| < e. X3

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