Problem

Use universal modus tollens to fill in valid conclusions for the argument.Universal ModusT...

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

All irrational numbers are real numbers

is not a real number.

∴ _____

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Solutions For Problems in Chapter 3.4

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