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Discrete Mathematics An Open Introduction, 4th Edition

Oscar Levin

Worksheet Preview Activity
A4US

1.
Consider the statement, “Whenever Holmes wears a purple shirt and the green vest, he chooses to not wear a bow tie.” Let P be the statement, “Holmes wears a purple shirt,” G be the statement, “Holmes wears the green vest,” and B be the statement, “Holmes wears a bow tie.” Which of the following is the best translation of the statement into propositional logic?
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2.
Consider the statement, “Holmes never wears the green vest unless he is also wearing either a purple shirt or red shoes.” With P and G as in the previous question, and R being the statement, “Holmes wears red shoes,” which of the following is the best translation of the statement into propositional logic?
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  • G→(P∨R)
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  • ¬G→(P∨R)
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  • Consider the case where Holmes does wear a green vest but does not wear a purple shirt or red shoes. That would make ¬G false and P∨R true, so the implication would be true. But in this situation, the original statement would be false.
  • (P∨R)→G
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  • Consider the case where Holmes does not wear a purple shirt or red shoes, and does wear the green vest. That would make P∨R false and G true, so the implication would be true. But in this situation, the original statement would be false.
  • (P∨R)→¬G
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  • Consider the case where Holmes does not wear a purple shirt or red shoes, and does wear the green vest. That would make P∨R false and ¬G false, so the implication would be true. But in this situation, the original statement would be false.
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3.
Consider the statement, “If you major in math, then you will get a high-paying job,” and the statement, “Either you don’t major in math, or you will get a high-paying job.” In which of the following cases are both statements true? Select all that apply.
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  • You major in math and get a high-paying job.
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  • You major in math and don’t get a high-paying job.
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  • In fact, in this case, both of the statements are false.
  • You don’t major in math and do get a high-paying job.
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  • This makes the implication true because the if part is false. The disjunction is true because the first part is true.
  • You don’t major in math and don’t get a high-paying job.
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