MATH15Amidtermsol

MATH15Amidtermsol - Name(Last First Please circle your...

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Name (Last, First) SOLUTIONS Please circle your section: A01 A02 A03 A04 5 PM 6 PM 7 PM 8 PM Math 15A Midterm Briggs Fall Quarter 2004 No books, notes, calculators, or any unauthorized assistance is permitted on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. To receive full credit on your proofs, please comply with the writing guidelines as discussed in class. If a question is not clear, ask for clarification. GOOD LUCK! 1. ( 15 points ) Determine whether the following argument is valid. P ( Q R ) P ∨ ∼ Q R Q Q Solution: An argument form is valid provided that the truth of the premises guarantee the truth of the conclusion. We see in the following truth table for the given argument form, there are four cases in which all three premises are true, denoted by “critical row”. Because there are instances in which all three premises are true and the conclusion is false, the argument is INVALID. premise premise premise conclusion P Q R Q R Q P ( Q R ) P ∨ ∼ Q Q T T T F T T T T T T F F T T T T T F T T T T T F T F F T F F T F F T T F T T F T F T F F T T F T F F T T T T T F F F F T F T T F ←- critical row ←- critical row ←- critical row ←- critical row
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