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Exam 3: Introduction to Logic

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Question 51

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$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If $7 x + 2 y > 6$ , the answer is "Sea."

A) $7 x + 2 y > - 6$ so the answer is not "Sea."
B) $7 x + 2 y \leq 6$ and the answer is not "Sea."
C) If $7 x + 2 y > 6$ , the answer is not "Sea."
D) $7 x + 2 y > 6$ and the answer is not "Sea."

E) C) and D)
F) None of the above

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Question 52

True/False

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

A) True
B) False

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Question 53

Multiple Choice

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Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it is cold, then you need a coat. $\underline { \text {You do not need a coat} }$ It is not cold.

Construct a truth table for the statement. - $(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})$

Determine whether the argument is valid or invalid. -If you are infected with the measles, then it can be transmitted. The results are grave and it cannot be transmitted. Therefore, if the results are not grave, then you are infected with the measles

Solve the Sudoku. -Hard $\begin{array} { | l | l | l | l | l | l | l | l | l | } \hline & 8 & & & & 6 & 7 & & 5 \\\hline & & & & 9 & & & 8 & \\\hline 3 & & & & 8 & & & & \\\hline 9 & & 5 & & & & 2 & & \\\hline & 3 & & 9 & 6 & 1 & & 5 & \\\hline & & 4 & & & & 9 & & 8 \\\hline & & & & 3 & & & & 2 \\\hline & 6 & & & 7 & & & & \\\hline 7 & & 9 & 6 & & & & 3 & \\\hline\end{array}$

Tell whether the conditional statement is true or false. -Here F represents a false statement. $\mathrm { F } \rightarrow ( 5 = 8 )$

Find the truth value of the statement. - $7 - 5 = 2 \text { if and only if } 11 + 2 = 14$

Tell whether the conditional statement is true or false. - $( 8 = 12 - 4 ) \rightarrow ( 5 > 0 )$

Write a negation of the inequality. Do not use a slash symbol. - $x \geq - 50$

Write a logical statement representing the following circuit. Simplify when possible. - $\sim p \rightarrow [ ( q \wedge r ) \vee \sim p ]$

$\text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. }$

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.

Tell whether the conditional statement is true or false. -Here F represents a false statement. $( 2 = 2 ) \rightarrow F$

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both". - $8 + 4 = 20 \underline\vee 3 + 5 = 13$

Decide whether the statement is compound. -I'll go to Mexico or Costa Rica for my next vacation.

Solve the logic puzzle by using a grid. -The scores of a math test for five students were posted on the bulletin board. The students' names are Tom, Penny, Jim, John and Fred. Tom and Fred scored the same number of points. Penny did Not get the highest score. John's score was 5 points lower than Jim's. The scores were 69, 52, 94, 52 And 89. Which student received what score?

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it's Tuesday, then this must be Paris. $\underline { \text {Today is Wednesday.} }$ This cannot be Paris.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim \mathrm { p} \vee ( \mathrm {~q} \wedge \sim \mathrm { r } )$

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