Exam 3: Introduction to Logic

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim does not play football or Michael does not play basketball.

Use an Euler diagram to determine whether the argument is valid or invalid. -All students who study get better grades. $\underline { \text { Roger is a student who studies.} }$ Roger will get better grades.

Label the pair of statements as either contrary or consistent. -She is unemployed. She is working at the local hospital.

Tell whether the conditional statement is true or false. -Here F represents a false statement. $( 9 < 5 ) \rightarrow F$

$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$ - $( \sim p \wedge q ) \vee \sim r$

Write the compound statement in words. Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." - $\sim ( p \rightarrow q )$

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If you can't take the heat, stay out of the kitchen.

Rewrite the statement in the form "if p, then q". -I will lose weight if I diet.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -You get soup or you get salad. $\underline { \text {You did not get soup.} }$ You got salad.

If a conditional statement is false, its consequent must be false.

Use De Morgan's laws to write the negation of the statement. -A day late and a dollar short.

Use a truth table to determine whether the argument is valid. -

Construct a truth table for the statement. - $p \rightarrow \sim\ q$

Construct a truth table for the statement. - $\sim ( p \rightarrow q ) \rightarrow ( p \wedge \sim q )$

The argument has a true conclusion. Identify the argument as valid or invalid. -A square is a parallelogram. $\underline { \text {A square has four sides.} }$ A parallelogram has four sides.

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -I'll exercise if I eat too much.

Write an equivalent statement that does not use the if ... then connec $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$ -If he isn't strong enough to hold the bat, then he can't play with us.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No cars come from Iceland.

Write the compound statement in words. Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." - $p \rightarrow$ r