Math 10 Name Exam 1: Chapters 2 and 5

Points are as stated. Y o u must s h o w a l l w o r k to receive ful l credit.

State whether each statement is true or false. Points are ' a l l or nothing ' for tme false. 2 points each.

1. The set of all the best movies is a well defined set.

2. The set of words in a dictionary is a well defined set.

3. {freshman, sophomore, junior, senior} is equal to {9* , lO''^, 11^, 12*}

4. {cat, dog, rat, bird } is equivalent to {dog, bird, cat, kangaroo}

5. {2,4,6,8,...} c {1,2,3,4,...}

6. {1,2,3,4,...} c {2,4,6,8,...}

7. { }e {1,2,3,4,...}

8. { } c {1,2,3,4,...}

9. { } ^ { }

10. 0 e { }

11. I f M e A^,andM3A^,then M =

12. {x\x e N and x < 6} c {x | x e A' and x < 5}

13. {x I X e TV and X > 6} = {6,7,8,...}

14. For any set , Ar\A'={ }

15. For any set ^ , Af]A'=U .

16. For any set^ ,U-A'=A.

17. The set^ = {red,blue, green, purple}, has cardinality/7(yi) = 2'' = 16 .

18. Set^ = {a,b,c}, set5 = {1,2} , 5 x ^ = {(a,l),(a,2),(Z>,]),(d,2),(c,l),(c,2)} .

19. Set^ = {x I X e alphabet }, setfi = {x | x e consonants }^A-B-{x\xe vowels}.

20. The set A = {chocolate ,slrawberry ,vanilla }, has 7 proper subsets.

21. Express the set in roster form, w o n h 4 points.

{ x | x e T V a n d - | < x < | } ^ \ / Z - * ^

22. Express the set in set builder form, wonh 4 points.

(red, orange, yellow, blue,...} ^ ^ y'y^ ^ C c \ c X ' 5 ^

23. Let set A = {red, blue} and set B = {green}, find BxA. w o r t h 2 pomts.

24. For the following problems, use the information to fill in the Venn diagram and answer the questions. W o r t h 2 points each.

f /={l ,2 ,3 ,4 ,5 ,6 , 7, 8,9,10} ^={2,3,4,5,9} fi={l,3,6, 7,9} C={1,2,5,6,8,9}

a. Find A'f]B. &

b. Find A'HB'.

c. Find A[)iBf]Cy.

d Fina /in<B'UC'),

g. Find the otsti'nct number subsets of U. ^

h. Find the distinct number of proper subsets of U. ' U l U. J L

25. A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options air conditioning, radio and power windows were already installed. The survey found: W o r t h 2 points each.

15 had air conditioning 2 had air conditioning and power windows but no radios 12 had radio 6 had air conditioning and radio but no power windows 11 had power windows 4 had radio and power windows 3 had all three options.

Construct a Venn diagram and then determine a) the number of cars that have none of these items.

b) the number of cars that have at least two of these items. m c) the number of cars that only have air conditioning.

d) the number of cars that only have a radio.

e) the number of cars that only have power windows.

26. Draw Venn diagrams to determine whether A [j {B [j 0')'= A [j (B' f] C)for all setSv4, B, and C. Show your work. Wonh 6 points.

U Power

Air Conditioning

27. At Wilson High School 25 girls participate in soccer, 33 girls participate in basketball, and 43 girls participate in either soccer or basketball. How many girls participate in both soccer and basketball? W o r t h 4 points.

28. Show that the set {3, 9, 27, 81,...} has a cardinality of K„, by determining which set shows a one-to-one correspondence with the Natural numbers, wonh 2 points.

A){ I, -1 -> 4, . n, ...} ( B) { 1, 2, 4, .. , n. i i i i -I i i i

{ 9, 27, 81. . ... n3, ...} { 3, 9, 27, 81, , 3", C) i i . 1 -> 4, . n, ...} D) { .1, 2, 3, 4, ..

\ i i i i i I I i i 3, 9, 27, 81, . .., 32n ...} { 3. 9, 27, 81, - , 3n,

1 3 — 29. Consider the following set of numbers. • - , VlO, -4.2, - 1 ^ , 0.6, 0, 3.9, VsT > W o r t h 1 point each.

a. List the rational numbers

b. List the irrational numbers

c. List the integers. —•— '

d. List the real numbers.

30. Determine whether each number is rational or irrational, w o r i h 1 p o i n t e a c h .

a) 0.023 K b) 0.6758674835476857467486718 ^ E c) V36

d) ^

31. State the property that each statement illustrates. W o r t h 1 point e a c h

a) 4(x+>.) = (4-x)+(4->') r\ tfM.W- yc> b) (4-x).3. = 4 .(x.; .) Sm^^V

c) 4 • (x + = (x + • 4

d) 4 + (x + >') = (x + >') + 4