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Unformatted text preview: .mmBm hammooom .2: :3 Beam .985 05 83 8 8338 mm 9%: EB sow
.803on Emowmo EN mm omw @805on cm 3838 Same mEH woom 6H 25m
H 243mm 02% 3:85: A. «EN gm oEmZ 1. Construct a Venn diagram, properly labeled, to determine the validity of the given arguments.
Please circle your answer. (8 points: 4 points each) 1). 1. No men can afford prescription drugs.
2. Teachers can afford rescri tion dru s.
Therefore, no teachers are men. not valid 2). 1. Some animals are dangerous. 2. A tiger is an animal. .
Therefore, a tiger is dangerous. valid II. Multiple choices, circle your answer. (21 points: 3 points each) 3). Find the negation of the following sentence:
Some of the cheese has mold
a. All of the cheese has mold.
None of the cheese has mold.
0. Some of the cheese does not have mold.
d. The cheese has mold. Using the symbolic representations
p: it is a holiday q: the school is closed. r: the weather is very bad. express the compound statements for problems 4 and 5 in symbolic form: 4). If the school is closed, it is a holiday or the weather is very bad.
a. q —> (p A r)
b. p —«> (~ q /\ r)
C53 q > (fr v r) d. pA(q—>r) 5). It isn't a holiday and the school is not closed. .~p/\~q
b. 6). If a compound statement consists of 4 individual statements, each represented by a different
letter, how many rows are required in the truth table? a. 4 b. 8 c. 12 16 7). Match the truth table below to the appropriate statement. Table 1: Truth Table a. p~>q
b. pAq
c. pvq ~qu 8). According to De Morgan's Law which of the following is equivalent to ~ (p /\ q) ?
a. p ~—> q b. p/\ ~ q @~pV~q Ed qA~p 9). Construct the negation of the following:
If I win the lottery, I will buy a new car.
a. If I don't win the lottery then I will not buy a new car.
b. I don't win the lottery and I will buy a new car.
win the lottery and I will not buy a new car.
. If I buy a new car, then I will win the lottery. III. Suppose the universal set is the set of aIIWthat are S 6. Let A be those that
are S 4, B be that are odd, C be that are even. Using the sets given above to answer questions 10 to 14. 10). State the universal set and sets A, B and C using the roster notation. (8 points) U={l/1,3.4;516 3
A={"2I5.4’3 = {i,a,55
C={2,4.63 11). State the following using the roster notation. (8 points) A’: AUC={'13~/3214',65
AnC= {1,45
AanC= :(Z 12). State the cardinal number. (4 points) n(A' = 2
n(B)= 3
n(U)= 6 n(AmBﬂC)= O 13). Use De Morgan's laws to ﬁnd the following set and illustrate it by shading the Venn
diagram appropriately. (7 points) (AW = (A')' o 5’ v
2: A H P) l a : {A , 4. 6 i I
A o a = l >— , 4 5
14). Read the followin notation and circle all items that are true statements: (10 points) A g A F A c: B T A g C T
A'c; U r F {} c: U P 4 e B Cr) F
B=C r (13) n(A)=n(C) T (is) n(C)=n(B) (r) F
A = {x  x is a positive integer that is less than 5} F IV. By Use the following information for questions 15, 16 and 17. In a recent health survey, 750 single men in their twenties were asked to check the appropriate
box or boxs on the following form: ~ [3 I am a member of a private gym. El I am a vegetarian.
The results were tabulated as follows: 374 checked the gym box, 92 checked the vegetarian box,
and 332 were blank (no boxes were checked). (6“ (V) 15). Construct a Venn diagram illustrating the results of the survey. (8 points)
[21 I21 [I D
D 121 E El $51
“Lguv): 79'332 3448' Mathew
hm :— ‘iz Wwwwwmmu 16). What percent of the men were both members of a private gym and vegetarians? (5 points)
48
7:17 4 7; 17). What percent of the men were either members of a private gym or vegetarians? (5 points) 41 8 u M a 0. 55 :— 511 o m 1 7 V. Use the following information to answer questions 18 and 19. A group of 8 professors and 3 administrators must select a team of 6 people. How many teams
are possible if the team must consist of 18). 4 professors and 2 administrators? (7 points) 8.? a} a 801362 3 4M“)? 3454)! 19). less administrators than professors (hint: a team may consist of no administrator)? (9 points) 11 3% aolmmsmim ﬁ 0 8C6 + 865'5Ct f gca‘ ac; 5  4’ 2 V. Bonus problem. (5 points) 20). Construct a truth table to determine Whether the statements in the following pair are
equivalent. The streets are wet and it is not raining.
If it is raining, then the streets are wet. ...
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This note was uploaded on 02/05/2012 for the course MAT 110 taught by Professor Staff during the Summer '08 term at S. Alabama.
 Summer '08
 Staff
 Math

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