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

CMSC 250

Quiz #11

Monday, Nov. 19, 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.

[10 pnts.] Let $A = \{2,3,4,5\}$ and let $B = \{4,5,6,7,8\}$ . Let $S:A \rightarrow B$ be defined by

$\begin{displaymath} \forall (a,b) \in A \times B, (a,b) \in S \leftrightarrow a \mbox{ divides } b \end{displaymath}$

Explicitly state the elements of . ANSWSER:
$S = \{(4,4),(5,5),(2,4),(2,6),(2,8),(3,6),(4,8)\}$
GRADING:
-1 for any one element of the set missing
-1 for any that are there that shouldn't be to a max of -10
[10 pnts.] Indicate with a ``YES'' or ``NO'' in each blank if the following relations are Reflexive, Symmetric, and/or Transitive. Assume all are relations over the set . GRADING:
-1 for each incorrect answer (or blank answer)
-1 if didn't use yes and no
1. 1. YES Reflexive
  2. YES Symmetric
  3. NO Transitive
2. 1. NO Reflexive
  2. NO Symmetric
  3. YES Transitive
3. 1. YES Reflexive
  2. YES Symmetric
  3. YES Transitive
[10 pnts.] Let $M = \{1,2,3,4,5\}$ and let $R: M \rightarrow M$ be defined as

$\begin{displaymath} R = \{(1,3),(2,2),(3,1),(3,2),(3,3),(1,1),(4,5)\} \end{displaymath}$

Give the list of the elements in the set R' (the transitive closure of R). ANSWER: $R' = R \union \{(1,2)\}$
or
$R' = \{(1,3),(2,2),(3,1),(3,3),(1,1),(4,5),(3,2),(1,2)\}$
GRADING:
up to -5 for missing elements that were in R
-3 if the (1,2) is not added
-2 for anything else added