Name (PRINTED):
Student ID #:
Section # (or TA's:
name and time)

CMSC 250

Quiz #1

Monday, Sept. 10, 2001

Write all answers legibly in the space provided. The number of points possible for each question is indicated in square brackets - the total number of points on the quiz is 30, and you will have exactly 15 minutes to complete this quiz. You may not use calculators, textbooks or any other aids during this quiz.

1. [10 pnts.]Determine if each of the following pair of statements is logically equivalent by using a truth table. Use 1 for ``true'' and 0 for ``false'' to complete the truth table.
   1. $(p \wedge q) \vee r$
   2. $(p \vee r) \wedge (q \vee r)$

   (Yes or No) These statements are logically equivalent.

2. [10 pnts.]Give one possible value for the $n$ expressed in each of the following which would make the statement true. (If there is no possible value, write the word ``impossible''.)
   • p = $(n \geq 1)$
   • q = $(n = 3)$
   • r = $(n \leq 7)$
   1. $\sim (p \vee \sim q)$
      
   2. $(p \wedge r) \wedge q$
      

   
   
   
   
   

   $\downarrow$ TURN OVER $\downarrow$

3. [10 pnts.]Write the contrapositive, converse and inverse of the following logical expression. Do not simplify the expression at all - just give the statement requested in the form you would get from the definition.
   
   $$(p \wedge q) \rightarrow (r \vee p)$$
   
   

   contrapositive
   converse
   inverse

4. Give an alias - a madeup name you will associate with yourself - under which you would like your grades posted. If you do not want to have your grades posted, specify the alias ``None''.

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