Math 1090 Homework 1 Math 1090 Homework 1
Due September 22 at Noon.

  1. In translating each of the following to symbolic form, the word ``or'' would be replaced by or \veebar . What is the appropriate choice in each case? Explain why your choice is correct.

    1. To take discrete mathematics, you must have taken calculus or a course in computer science.
    2. Dinner for two includes two items from column A or three items from column B.
    3. When you buy a new car from Acme Motor Company, you get $ 2000 back in cash or a 2% car loan.
    4. School is closed if more than 2 feet of snow falls or if the wind chill is below -50.

  2. Determine whether
    ( ~ q (p q))   ~ p
    is a tautology.
  3. Does p q logically imply (pq)  ~ p ? Justify your answer.
  4. Use truth tables to show that both
    p (p q)  and  p (p q)
    are equivalent to p.
  5. Determine whether
    (p q) r   and  p (q r )
    are equivalent.
    1. Determine whether
      (p q) r   and  p (q r )
      are equivalent.
    2. Is ((p q) r)     (p (q r )) a tautology? Explain.


File translated from TEX by TTH, version 2.60.
On 27 Aug 2000, 11:41.