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 Ú 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 Ù(p ® q)) ®   ~ p
is a tautology.
3. Does p ® q logically imply (pÙq) Ú ~ p ? Justify your answer.
4. Use truth tables to show that both
 p Ú(p Ùq)  and  p Ù(p Úq)
are equivalent to p.
5. Determine whether
 (p Úq) ® r   and  p Ú(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.