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 inflation continues, then interest rates will remain high. If inflation continues, then if interest rates remain high then business activity will decrease. If interest rates remain high, then if business activity decreases then unemployment will rise. So if unemployment rises, then infl ation will continue. ( I, H, D, U )