If any truth-functional argument is valid, we have the tools to prove it valid; and if it is invalid, we have the tools to prove it invalid. For each of the following arguments determine whether it is valid or invalid using the STTT. If it is valid, prove it valid using the nineteen rules of inference. These proofs will be more difficult to construct than in preceding exercises, but they will offer greater satisfaction.

If taxes are reduced, then inflation will rise, but if the budget is balanced, then unemployment will increase. If the president keeps his campaign promises, then either taxes are reduced or the budget is balanced. Therefore if the president keeps his campaign promises, then either inflation will rise or unemployment will increase. (T, I, B, U, K)