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 either it will rain tomorrow or it won’t rain tomorrow, then weather predicting is an exact science. Therefore weather predicting is an exact science. (R, W)