Exam 3: Logic

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -If people drive small cars then people will use less fuel and the ozone hole will not expand.

Determine which, if any, of the three statements are equivalent. -I. If the house is not white, then the house is not small. II. The house is not white and the house is small. III. It is false that the house is white or that the house is not small.

Write the compound statement in words. -Let $\mathrm { p } =$ "The monitor is included." $\mathrm { q } =$ "The color printer is optional." $\mathrm { r } =$ "The zip drive is extra." $\mathrm { q } \leftrightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $[ ( p \rightarrow q ) \wedge ( q \rightarrow r ) ] \rightarrow ( p - r )$

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. -If 10 does not divide the counting number, then 5 does not divide the counting number.

Identify the standard form of the argument. - \rightarrow \rightarrow \therefore\rightarrow

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -In Region X, people are spending more on leisure activities. Annual per capita spending in dollars: 2000 2010 Movies 31 192 Dining Out 97 494 Vacations 514 1355 Sporting Goods 154 305 The average person in Region X spent $192 on the movies in 2010, and the average person in Region X spent $154 on sporting goods in 2010.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is good and if I eat too much, then Iʹll exercise.

Use truth tables to test the validity of the argument. - \wedge\sim \vee \therefore

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The car is in the garage and the bicycle is in the driveway.

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -Pat Rabbit did not go into Mr. McNoodleʹs garden and Molly collected blueberries.

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $( p \vee q ) \wedge \sim q$

Convert the compound statement into words. - $\mathrm { p } =$ "Babies eat bananas." $q =$ "Babies wear plastic bibs." $\mathrm { p } \vee \mathrm { q }$

Use the information given in the chart or graph to determine the truth values of the simple statements. Then determine the truth value of the compound statement given. - Planet X \bullet Moon 1 o Moon 2 Diameter of moons: May have: o Moon 3 \circ5-8 o water ice \circ Moon 4 \circ9-19 \bullet atmosphere \circ Moon 5 \bullet20-26 oboth Moon 2 has a diameter of 5-8 km and Moon 4 may have an atmosphere, or Moon 5 does not have a diameter of 9-19 km.

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

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I exercise, then the food wonʹt be good and I wonʹt eat too much.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football and Michael plays basketball.

Write the compound statement in symbols. Then construct a truth table for the symbolic statement. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I exercise, then the food won?t be good and I won?t eat too much.

Write a negation of the statement. -All dinosaurs were carnivores.

Convert the compound statement into words. - $\mathrm { p } =$ "People buy large houses." $q =$ "Fossil fuels pollute the air." $q \wedge p$