Use universal modus tollens to fill in valid conclusions for the argument.
Universal ModusTollens
Another crucially important rule of inference is universal modus tollens.Its validity results from combining universal instantiation with modus tollens. Universal modus tollens is the heart of proof of contradiction, which is one of the most important methods of mathematical argument.
Universal Modus Tollens | |
Formal Version | Informal Version |
∀x, if P(x) then Q(x). | If xmakes P(x) true, then xmakes Q(x) true. |
~Q(a), for a particular a | a does not make Q(x) true. |
∴ ~P(a). | ∴ a does not make P(x) true. |
Exercise
If a computer program is correct, then compilation of the program does not produce error messages.
Compilation of this program produces error messages.
∴ _____
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