Elementary Mathematics: Laws of Logic
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Elementary Mathematics: Laws of Logic

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Questions and Answers

Which law is used to rewrite the statement ~p ∨ q → r ∨ ~q?

  • Commutative law of ∧
  • Associative law of ∨
  • Implication law (correct)
  • De Morgan's law

    • What is the equivalent form of p→q using De Morgan's law?

  • ~p ∨ q
  • p ∧ ~q
  • ~(p ∧ ~q) (correct)
  • p ∨ ~q

    • Which of the following is a tautology?

  • p → ~(p→q)
  • ~(p→q) → p (correct)
  • ~(p→q) ∧ p
  • p ∧ ~(p→q)

    • If p→q is false, what is the truth value of ~p → q?

    <p>True</p> Signup and view all the answers

    What is the equivalent form of (p→r)↔(q →r)?

    <p>(~p ∨ r)↔(~q ∨ r)</p> Signup and view all the answers

    What is the equivalent form of p→q using the implication law?

    <p>~p ∨ q</p> Signup and view all the answers

    If p→q is false, what is the truth value of p ∨ q?

    <p>True</p> Signup and view all the answers

    What is the equivalent form of ~(p→q) using the implication law?

    <p>p ∧ ~q</p> Signup and view all the answers

    What is the equivalent form of (p→r)↔(q →r) using the implication law?

    <p>(~p ∨ r)↔(~q ∨ r)</p> Signup and view all the answers

    Is the argument 'An interesting teacher keeps me awake. I stay awake in Discrete Mathematics class. Therefore, my Discrete Mathematics teacher is interesting.' valid?

    <p>No</p> Signup and view all the answers

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