Imagine that you have acquired a program for logical computations. It can analyze and construct proofs using predicate-logical expressions.
You decide to use your program to prove all the theorems in the chapter about graph theory (both those in the text and those in the exercises). In order to do this you want to start by defining predicates that can be useful in this context, and express the theorems using these predicates.
Define a number of predicates that can be relevant in this context (try to make both $monadic$, $dyadic$ and $triadic^2$ ones) and express some of the theorems in the chapter using these predicates.
How would I solve the question ?
Inclue the set membership predicate $\in$ and add set theory axioms. With that you can construct predicates like graph, edge, vertex.