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5.9: Exercises

  • Page ID
    113165
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    5.1: Logic Statements

    1. Write the negation of the quantified statement: "Everyone failed the quiz today".

    2. Write the negation of the quantified statement: "Someone in the car needs to use the restroom".

    3. Translate each statement from symbolic notation into English sentences. Let A represent “Elvis is alive” and let G represent “Elvis gained weight”.

    1. \(A \vee G\)
    2. \(\sim(A \wedge G)\)
    3. \(G \rightarrow \sim A\)
    4. \(A \leftrightarrow \sim G\)

    5.2: Truth Tables- Conjunction (and), Disjunction (or), Negation (not)

    4. Create a truth table for the statement: \(A\ \wedge \sim B\)

    5. Create a truth table for the statement: \(\sim(\sim A \vee B)\)

    6. Go back and look at the truth tables in Exercises 4 & 5. Explain why the results are identical.

    7. Complete the truth table for \((A \vee B) \wedge \sim(A \wedge B)\).

    \(\begin{array}{|c|c|c|c|c|c|}
    \hline A & B & A \vee B & A \wedge B & \sim(A \wedge B) & (A \vee B) \wedge \sim(A \wedge B) \\
    \hline \mathrm{T} & \mathrm{T} & & & & \\
    \hline \mathrm{T} & \mathrm{F} & & & & \\
    \hline \mathrm{F} & \mathrm{T} & & & & \\
    \hline \mathrm{F} & \mathrm{F} & & & & \\
    \hline
    \end{array}\)

    8. For each situation, decide whether the “or” is most likely exclusive or inclusive.

    1. An entrée at a restaurant includes soup or a salad.
    2. You should bring an umbrella or a raincoat with you.
    3. We can keep driving on I-5 or get on I-405 at the next exit.
    4. You should save this document on your computer or a flash drive.

    9. Use De Morgan’s Laws to rewrite each conjunction as a disjunction, or each disjunction as a conjunction: It is not true that Tina likes Sprite or 7-Up.

    10. Use De Morgan’s Laws to rewrite each conjunction as a disjunction, or each disjunction as a conjunction: It is not the case that you need a dated receipt and your credit card to return this item.

    5.3: Truth Tables- Conditional, Biconditional

    1. Create a truth table for the statement: \((A \wedge B) \rightarrow C\)

    2. Create a truth table for the statement: \((A \vee B) \rightarrow \sim C\)

    3. Consider the statement “If you are under age 17, then you cannot attend this movie.”

    1. Write the converse.
    2. Write the inverse.
    3. Write the contrapositive.

    4. Assume that the statement “If you swear, then you will get your mouth washed out with soap” is true. Which of the following statements must also be true?

    1. If you don’t swear, then you won’t get your mouth washed out with soap.
    2. If you don’t get your mouth washed out with soap, then you didn’t swear.
    3. If you get your mouth washed out with soap, then you swore.

    5. Write the negation of the conditional statement: If you don’t look both ways before crossing the street, then you will get hit by a car.

    6. Write the negation of the conditional statement: If Luke faces Vader, then Obi-Wan cannot interfere.

    7. Write the negation of the conditional statement: If you weren’t talking, then you wouldn’t have missed the instructions.

    8. Assume that the biconditional statement “You will play in the game if and only if you attend all practices this week” is true. Which of the following situations could happen?

    1. You attended all practices this week and didn’t play in the game.
    2. You didn’t attend all practices this week and played in the game.
    3. You didn’t attend all practices this week and didn’t play in the game.

    5.4: Arguments with Truth Tables

    5.5: Forms of Valid and Invalid Arguments

    5.6: Arguments with Euler Diagrams

    For questions 23-28, use a Venn diagram or truth table or common form of an argument to decide whether each argument is valid or invalid.

    1. If a person is on this reality show, they must be self-absorbed. Laura is not self-absorbed. Therefore, Laura cannot be on this reality show.

    2. If you are a triathlete, then you have outstanding endurance. LeBron James is not a triathlete. Therefore, LeBron does not have outstanding endurance.

    3. Jamie must scrub the toilets or hose down the garbage cans. Jamie refuses to scrub the toilets. Therefore, Jamie will hose down the garbage cans.

    4. Some of these kids are rude. Jimmy is one of these kids. Therefore, Jimmy is rude!

    5. Every student brought a pencil or a pen. Marcie brought a pencil. Therefore, Marcie did not bring a pen.

    6. If a creature is a chimpanzee, then it is a primate. If a creature is a primate, then it is a mammal. Bobo is a mammal. Therefore, Bobo is a chimpanzee.

    5.7: Logical Fallacies in Common Language

    1. Name the type of logical fallacy being used: If you don’t want to drive from Boston to New York, then you will have to take the train.

    2. Name the type of logical fallacy being used: New England Patriots quarterback Tom Brady likes his footballs slightly underinflated. The “Cheatriots” have a history of bending or breaking the rules, so Brady must have told the equipment manager to make sure that the footballs were underinflated.

    3. Name the type of logical fallacy being used: Whenever our smoke detector beeps, my kids eat cereal for dinner. The loud beeping sound must make them want to eat cereal for some reason.


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