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1. Express the following in roster form: Set M is the set of natural numbers between thirteen and twenty-one.

M = {14, 15, 16, 17, 18, 19, 20}

assuming that “between” doesn’t mean including the endpoints

2. Can the word "LIONS" be played from the letters I, E, N, L, S, T, R as the first move in a Scrabble game? Explain your answer.

No, because there is no O

3. Are the two sets equal, equivalent, neither or both? Explain your answer.

V = {cat, dog, bird, flea}; W = {bird, dog, cat, mouse}

They aren’t equal, since one has flea and the other has mouse.

But they are equivalent, since they each have 4 elements.

4. Given the diagram below, find PUQ. Write in correct set notation. “Graph uploaded” #4

[pic]

Things in both P and Q:

{r, s, o, e, q, u, t}

5. Given U = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, A = {12, 14, 16, 18, 20}, and B = {11, 13, 14, 15, 18, 19, 20}.

Find A’ U B’ . Do not skip to the answer. Show your work, finding A’, then B’ then find their union.

A’ is the things not in A: {10, 11, 13, 15, 17, 19}

B’ is the things not in B: {10, 12, 16, 17}

Join those together: {10, 11, 12, 13, 15, 16, 17, 19}

6. Given the following sets, select the statement below that is NOT true. 

A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t}, E = {t, e, a}

       [pic]E ⊂ D E is the same size as D, so this is the NOT true one

       [pic]E ⊆ B

       [pic]D ⊆ A

       [pic]C ⊂ A

       [pic]D ⊂ B

7. Using correct mathematical notation and symbols, express the following in set builder notation: Z = {17, 18, 19, 20, 21, 22, 23, 24, 25} and submit it to the week 2, assignment 3 drop box.

Z = {x | x [pic]Z, 17 ≤ x ≤ 25}

8. A car dealership interviewed every driver who came onto their lot on Tuesday. This produced the following results: there were 31 people who owned trucks and 62 people who owned cars. If 22 people owned both a truck and a car and 9 people owned neither, how many people were interviewed?

N(total) = N(A) + N(B) – N(AandB) + N(neither)

= 31 + 62 – 22 + 9

= 80

9. An electronics store surveyed every 11th customer who came onto the store for a week.

Of the 375 people who responded,

 

181 people watched movies on VHS tapes

245 people watched movies on DVDs.

66 people watched movies both on VHS tapes and DVDs.

 

Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the Week 2, assignment 3 drop box. Use your diagram to answer the following questions here.

[pic]

 

i. Of those surveyed, how many watched only VHS tapes? 115

ii. Of those surveyed, how many watched only DVDs?  179

iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both? 115+179 = 294

iv. Of those surveyed, how many watched VHS tapes or DVDs, or both? 375-15 = 360

10. A survey of fruit tree growers showed the following:

 

59 grew raspberries     23 grew both raspberries and blueberries 

50 grew blueberries     11 grew both raspberries and strawberries

27 grew strawberries    14 grew both blueberries and strawberries

9 grew all three types       13 grew none of these three

 

 

Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the Week 2, assignment 3 drop box. Use your diagram to answer the following questions here.

 

[pic]

(a)   How many grew only blueberries? 22

(b)   How many grew both raspberries and blueberries, but not strawberries? 14

(c)   How many grew only raspberries? 34

(d)   How many grew none of these three or only strawberries?

11+13 = 24

(e)   How many fruit tree growers were surveyed?

34+14+22+2+9+5+11+13 = 110

11. In a survey of 100 dancers, 53 knew the Salsa, 68 knew the Merengue, and 47 knew the Cha Cha. Of these, 41 knew the Merengue and Salsa dances, 28 knew the Salsa and Cha Cha, and 37 knew the Merengue and Cha Cha. Twenty-five dancers knew all three dances.

 

Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the Week 2, assignment 3 drop box. Use your diagram to answer the following questions here.

 

[pic]

(a)   How many knew only the Merengue? 15

(b)   How many knew only the Cha Cha? 7

(c)   How many knew exactly one of the three dances? 9+15+7 = 31

(d)   How many knew the Merengue and Salsa, but not the Cha Cha? 16

(e)   How many knew none of these dances? 13

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