5.4: Activities

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Activity \(\PageIndex{1}\)

Write an argument in English that has modus ponens form where at least one premise is false, and the conclusion is true.

Does your argument contradict the fact that every modus ponens argument is valid?
Write an argument in English that has modus tollens form where at least one premises is false and the conclusion is false. Does your argument contradict the fact that every modus tollens argument is valid?
Write an argument in English that has syllogistic form where all the premises are true. Is your conclusion true or false?

Activity \(\PageIndex{2}\)

Prove that modus tollens is valid without using a truth table. Instead, use the following facts:

modus ponens is valid; and
a conditional is equivalent to its contrapositive.

Activity \(\PageIndex{3}\)

Discuss why an argument being valid is equivalent to its premises logically implying its conclusion.

Activity \(\PageIndex{4}\)

The definition of valid argument is as follows.

Whenever the premises are all true, the conclusion is true as well.

Create an equivalent definition that is the contrapositive of the definition above.

Activity \(\PageIndex{5}\)

Show that the following argument is valid without using a truth table. Instead, argue that the argument fulfills the equivalent definition for valid argument that you created in Activity \(\PageIndex{4}\).

\(\begin{aligned} &p \rightarrow \neg q \\ &r \rightarrow (p \land q) \\ & \hline \neg r \end{aligned}\)