Are the following arguments valid, and if so, symbolize and offer proof using all the rules of symbolic logic (using truth-functional tables and boolean logic): If the Monetarists are correct, then there is an increase in inflation IFF the money supply increases too fast. If the Keynesians are correct, then there is an increase in inflation IFF there is a decrease in unemployment. If the Libertarians are correct, there is an increase in inflation IFF the federal government spends more than it takes in. The money supply increases too fast only if taxes are too low, and the federal government spends more than it takes in only if taxes are too low. There is no decrease in unemployment and taxes are not too low, but there is an increase in inflation. Therefore, neither the Monetarists, the Keynesians, nor the Libertarians are correct.