1. Find an inductive definition for each set S. In this question, N is the set...

 

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1. Find an inductive definition for each set S. In this question, N is the set of Natural numbers and includes 0. a) S: {1, 5, 13, 29, 61, ...} b) A = {0, 2, 4, 6, 8, ...} {0, 11, 22, 33, 44, ...} c) S: {amb | m,neN, where m,n > 0} * S is a set of strings m d) S = {a" (bc)" | m, n = N} e) S: { <1>, <3,1>, <9, 3, 1>, <27,9, 3, 1>,...} * S is a set of lists 1. Find an inductive definition for each set S. In this question, N is the set of Natural numbers and includes 0. a) S: {1, 5, 13, 29, 61, ...} b) A = {0, 2, 4, 6, 8, ...} {0, 11, 22, 33, 44, ...} c) S: {amb | m,neN, where m,n > 0} * S is a set of strings m d) S = {a" (bc)" | m, n = N} e) S: { <1>, <3,1>, <9, 3, 1>, <27,9, 3, 1>,...} * S is a set of lists

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a S 1 5 13 29 61 Base Case 1 is in S Recursive Step If k is in S then k 4 add 4 is also in S b A 0 2 ... View the full answer