Use universal modus tollens to fill in a valid conclusion fo

Use universal modus tollens to fill in a valid conclusion for the following argument.

All irrational numbers are real numbers.

is not a real number.

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Use the definitions of even and odd to justify your answer to the following question.

Assume that r and s are particular integers. Is 6r +4s2 +3 odd?

Prove the following statement using a constructive proof of existence.

There are distinct integers m and n such that is an integer.

Solution

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Using universal modus tollens

All irrational numbers are real numbers.

1/0 is not a real number.(giving an appropriate fallacy)

___All irrational numbers are not real numbers.(giving a not of the proposition)