Recall that, by definition, {A1,A2,,An}A if and only if every model of {A1,A2,,An} is a model of A. (a) What does it mean for an interpretation I to be a model of {A1,A2,,An} ? (b) In class, we said that {A1,A2,,An}A if and only if A1A2AnA is valid. In parts (b) and (c) of this question, you will justify this statement. First, suppose that every model of {A1,A2,,An} is a model for A. Under this assumption, show that A1A2AnA is valid. (Hint: Let I be an arbitrary interpretation and show that vI(A1A2AnA)=T.) (c) Now suppose that A1A2AnA is valid. Under this assumption, show that any model of {A1,A2,,An} is a model of A. (Hint: Let I be an arbitrary model of {A1,A2,,An} and show that I must also be a model of A.)