Consider a symbol vocabulary that contains c constant symbols, p k predicate symbols of

each arity k$,$ and f k function symbols of each arity k$,$ where $1<=$ k $<=$ A$.$ Let the domain size

be fixed at D$.$ For any given interpretation$$model combination, each predicate or function

symbol is mapped onto a relation or function, respectively, of the same arity. You may assume

that the functions in the model allow some input tuples to have no value for the function $($i$.$e$.,$

the value is the invisible object$).$ Derive a formula for the number of possible interpretation$$

model combinations for a domain with D elements. Don$$t worry about eliminating redundant

combinations.