Unformatted text preview: q and r. ..) Then establish the validity of the argument or give a counterexample to show that it is invalid. If there is a chance of rain or her red headband is missing, then Lois will not mow her lawn. Whenever the temperature is over 80 degrees Fahrenheit, there is no chance for rain. Today the temperature is 85 degrees Fahrenheit and Lois is wearing her red headband. Therefore (sometime today) Lois will mow her lawn. 5) Consider the following quantified statements. Determine if they are true or not. Explain your answer. (Let the universe for x and y be the positive integers.) a) 2200 x 5 y [y > x] b) 5 x 2200 y [x > y] c) 2200 x [ (x > 4) ⇒ ( (x 2 – 2x – 3) > 5)] d) 5 x 5 y [ (3x + y = 20) ∧ (x + 2y = 20) ∧ (2x  y = 0)] 6) Prove that for all real numbers x, y and z, if x+y+z >= 60, then x>=20 or y>=20 or z>=20. (Hint: Try using the contrapositive. ..)...
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 Spring '09

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