4. Here is a "proof" that (2i - 1) = n2 + 1 for n > 1. Set up the variables: For each k > 1, let A be true if (21-1) = 62 +1. Induction step: We need to show that for all k > 1, Ak-1 Ak. If Ax-1 is false, the implication is immediately true. Let's show that it must be true by supposing that Ak-1 is true and showing can't be false in this case either. If Ak-1 is true, then k-121 - 1) = (k-1)2 +1. Then _1 = (k-1)2 +1+(2k-1) = (k2 - 2k + 1) +1+2k-1=k+ 1. Notice that we have forgotten about the base case. For each of the following state- ments, tell whether we have proved the statement true: (a) A134927 A 134928 (b) A1 A2 (c) A5 is true (d) Az is false (e) Does it follow from what we have proved that A5 A10? 4. Here is a "proof" that (2i - 1) = n2 + 1 for n > 1. Set up the variables: For each k > 1, let A be true if (21-1) = 62 +1. Induction step: We need to show that for all k > 1, Ak-1 Ak. If Ax-1 is false, the implication is immediately true. Let's show that it must be true by supposing that Ak-1 is true and showing can't be false in this case either. If Ak-1 is true, then k-121 - 1) = (k-1)2 +1. Then _1 = (k-1)2 +1+(2k-1) = (k2 - 2k + 1) +1+2k-1=k+ 1. Notice that we have forgotten about the base case. For each of the following state- ments, tell whether we have proved the statement true: (a) A134927 A 134928 (b) A1 A2 (c) A5 is true (d) Az is false (e) Does it follow from what we have proved that A5 A10