CSCI 2400/SENG 1010
Solutions for practice questions set 1014

  1. For each of the following, define suitable propositions and express the premise and the conclusion as a propositional formula. Then say which rule of inference (by name) is being used. Stay within propositional logic.
    1. Example. Joel is a mountain climber and a runner. Therefore, Joel is a runner. 
      p = Joel is a mountain climber
      q = Joel is a runner
      Premise: p ∧ q
      Conclusion: q
      Rule: Simplification

       

    2. Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials.
      p = Kangaroos live in Australia
      q = Kangaroos are marsupials
      Premise: p ∧ q
      Conclusion: q
      Rule: Simplification

       

    3. Linda is an excellent swimmer. If Linda is an excellent swimmer then she can work as a lifeguard. Therefore, Linda can work as a lifeguard.
      p = Linda is an excellent swimmer
      q = Linda can work as a lifeguard
      Premises: p, p → q
      Conclusion: q
      Rule: Modus ponens

       

    4. Steve will work at a computer company this summer. Therefore, either Steve will work at a computer company this summer or Steve will be a beach bum.
      p = Steve will work at a computer company this summer
      q = Steve will be a beach bum
      Premise: p
      Conclusion: p ∨ q
      Rule: Addition

       

    5. Either it is not less than 100 degrees today or the pollution is dangerous. It is less than 100 degrees outside today. Therefore, the pollution is dangerous.
      p = It is less not than 100 degrees today
      q = The pollution is dangerous
      Premises: p ∨ q, ¬p
      Conclusion: q
      Rule: Disjunctive syllogism

       

    6. If I work all night on this homework, then I can answer all of the exercises. If I answer all of the exercises then I will understand the material. Therefore, if I work all night on this homework, then I will understand the material.
      p = I work all night on this homework
      q = I can answer all of the exercises
      r = I will understand the material
      p → q, q → r
      therefore p → r
      Hypothetical syllogism