Problem 9: True or False? Determine which of the statements below are true and which statements are false, and justify your reasoning. 1. Each sentence o in a first-order language C either has a deduction from 0, or there is a structure in which it is false. 2. There is a theory T in a first-order language C such that T has an infinite model, but T does not have an uncountable model. 3. There is a countable structure A for a language C = {c, d, F, G} (where c, d are constant symbols and F, G are 2-place function symbols) that satisfies exactly the same sentences as the field of real numbers R = (R, 0, 1, +, .). . Let T be a complete theory, and let A and B be two models of T. Then a sentence o is true in A if and only if it is true in B. . Consider the language C = (e, o} and the set Egr = { VxVyVzxo (y oz) = (xoy) oz, Vxxoe = x, Vx3yxoy = e} of group axioms. The theory of sentences logically implied by Ear is complete