91Ó°ÊÓ

Express each statement in "if ... then" form. (More than one correct wording in "if... then" form may be possible.) Then write the statement's converse, inverse, and contrapositive. All senators are politicians.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I am tired or hungry, I cannot concentrate. I can concentrate. \(\therefore\) I am neither tired nor hungry.

In the Sixth Meditation, Descartes writes I first take notice here that there is a great difference between the mind and the body, in that the body, from its nature, is always divisible and the mind is completely indivisible. Descartes's argument can be expressed as follows: All bodies are divisible. No minds are divisible. Therefore, no minds are bodies. Use an Euler diagram to determine whether the argument is valid or invalid.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I watch Schindler's List and Milk, I am aware of the destructive nature of intolerance. Today I did not watch Schindler's List or I did not watch Milk. \(\therefore\) Today I am not aware of the destructive nature of intolerance.

In Symbolic Logic, Lewis Carroll presents the following argument: Babies are illogical. (All babies are illogical persons.) Illogical persons are despised. (All illogical persons are despised persons.) Nobody is despised who can manage a crocodile. (No persons who can manage crocodiles are despised persons.) Therefore, babies cannot manage crocodiles. Use an Euler diagram to determine whether the argument is valid or invalid.

Determine which, if any, of the three given statements are equivalent. You may use information about a conditional statement's converse, inverse, or contrapositive, De Morgan's laws, or truth tables. a. If the train is late, then I am not in class on time. b. The train is late or I am in class on time. c. If I am in class on time, then the train is not late.

Explain how to use Euler diagrams to determine whether or not an argument is valid.

Under what circumstances should Euler diagrams rather than truth tables be used to determine whether or not an argument is valid?

Use a truth table to determine whether each statement is a tautology, a self- contradiction, or neither. \((p \wedge q) \wedge(\sim p \vee \sim q)\)

Describe how to obtain the contrapositive of a conditional statement.