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Problem 3. Let C be the language 0, S, function symbol, and + is a binary function symbol. where 0 is a constant symbol, S is a unary (a) Let N be the C-structure with universe N = {0, 1,2, … } where 0N-0 and SN : N → N is the usual successor function and +N : N × N → N is the usual addition (that is, 3M (a) := a + 1 and +N(a, b) := a + b for all a, b N). Write down a variable-free term t, other than SSO, such that N t SSO). (Note that strings S1 and 2 are not L235 valid terms, since symbols 1 and 2 do not belong to the language L.)

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