Fill in the blank with either or to make the statement true. A) B)

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1 Edison College MGF 1106 Summer 2008 Practice Midterm Exam Dr. Schnackenberg If you do not agree with the given answers, choose "E" for "None of the above". MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Fill in the blank with either or to make the statement true. 1) 0 1) A) B) Express the set using the roster method. Remember that N represents the set of rational numbers. 2) {x x N and x lies between 1 and 5} 2) A) {2, 3, 4, 5} B) {2, 3, 4} C) {1, 2, 3, 4} D) {1, 2, 3, 4, 5} Place the various elements in the proper regions of the following Venn diagram. 3) Let U = {8, 9, 10, 11, 12, 13, 14} and A = {8, 9, 12}. Find A' and place the elements in the proper 3) region. A) A' = {10, 11, 13, 14} B) A' = {11, 12, 13, 14} C) A' = {8, 9, 12} D) A' = {8, 9, 10, 11, 12, 13, 14} 1

2 Let U = {21, 22, 23, 24,...}, A = {21, 22, 23, 24,..., 40}, B = {21, 22, 23, 24,..., 50}, C = {22, 24, 26, 28,...}, and D = {21, 23, 25, 27,...}. Use the roster method to write the following set. 4) C' 4) A) C' = {22, 24, 26, 28,...} B) C' = {21, 23, 25, 27,..., 39} C) C' = {21, 22, 23, 24,...} D) C' = {21, 23, 25, 27,...} Write or in the blank so that the resulting statement is true. 5) {4, 6, 8} {3, 4, 5, 6, 8} 5) A) B) Use,,, or both and to make a true statement. 6) {a, b} {z, a, y, b, x, c} 6) A) B) and C) D) Calculate the number of subsets and the number of proper subsets for the set. 7) {1, 3, 5, 7, 9, 11} 7) A) 63; 64 B) 64; 63 C) 63; 62 D) 62; 63 Use the formula for the number of subsets of a set with n elements to solve the problem. 8) A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the 8) situation, no engines, one engine, two engines, three engines, or all four engines can be sent to a fire. How many options does the dispatcher have for sending the fire engines to the scene of the caller? A) 7 B) 16 C) 15 D) 8 Use the Venn diagram to list the elements of the set in roster form. 9) 9) B A) {13, 17} B) {14, 16, 17} C) {11, 14} D) {12, 13, 15, 16, 17} Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 10) (A B)' 10) A) {s, u, w} B) {r, t, v, x} C) {t, v, x} D) {r, s, t, u, v, w, x, z} 2

3 11) A' (B C') 11) A) {q, r, s} B) {r, t, z} C) {q, s, u, v, x, y} D) {q, r, s, t, z} Use the Venn diagram shown to answer the question. 12) Which regions represent set D E? 12) A) II, V B) IV, V C) I, III, IV, VI D) VIII Use the accompanying Venn diagram that shows the number of elements in regions I through IV to answer the question. 13) 13) How many elements belong to set A but not set B? 7 A) 6 B) 7 C) 15 D) 16 Use the formula for the cardinal number of the union of two sets to solve the problem. 14) Set A contains 6 elements, set B contains 13 elements, and 4 elements are common to sets A and B. 14) How many elements are in A B? A) 15 B) 19 C) 16 D) 14 Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning. 15) All sisters are females. 15) A) At least one sister is a female. B) Some females are not sisters. C) There are no sisters that are not females. D) All females are not sisters. 3

4 16) Some orchids are not flowers. 16) A) Not all orchids are flowers. B) Some flowers are not orchids. C) All orchids are not flowers. D) All orchids are flowers. Write the negation of the qualified statement. (The negation should begin with "all," "some," or "none.") 17) Some professors are linguists. 17) A) All linguists are professors. B) Not all professors are linguists. C) No professors are linguists. D) No linguists are professors. Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 18) p: Spartacus is a film. 18) q: Rambo is a film. Spartacus is a film and Rambo is not a film. A) p ~ q B) p ~ q C) p q D) p ~ q 19) p: This is a hammer. 19) q: This is a tool. If this is not a hammer, then this is not a tool. A) p ~ q B) ~ p ~ q C) ~ q ~ p D) ~ p ~ q Given that p and q each represents a simple statement, write the indicated symbolic statement in words. 20) p: Darren admires Zoe 20) q: Zoe admires Darren ~ p q A) Darren and Zoe do not admire each other. B) Darren does not admire Zoe, or Zoe admires Darren. C) Darren does not admire Zoe, but Zoe admires Darren. D) It is not true that Darren admires Zoe and Zoe admires Darren. 4

5 Complete the truth table by filling in the required columns. 21) ~ (p q) 21) p q p q ~ (p q) T T T F F T F F A) p q p q ~ (p q) T T T F T F F T F T F T F F F T B) p q p q ~ (p q) T T T F T F F T F T F T F F F F C) p q p q ~ (p q) T T T F T F F T F T F T F F T F D) p q p q ~ (p q) T T T T T F F F F T F F F F F F Use the De Morgan law that states: ~(p q) is equivalent to ~ p ~ q to write an equivalent English statement for the statement. 22) It is not the case that a gun and a nose are both weapons. 22) A) A gun is a weapon but a nose is not. B) A gun is not a nose and a nose is not a weapon. C) guns are not noses. D) A gun is not a nose or a nose is not a weapon. 5

6 Construct a truth table for the statement. 23) ~ p ~ q 23) A) p q ~ p ~ q ~ p ~ q T T F T T T F F F T F T T T T F F T F F B) p q ~ p ~ q ~ p ~ q T T F F T T F F T T F T T F F F F T T T C) p q ~ p ~ q ~ p ~ q T T F F T T F F T F F T T F F F F T T T D) p q ~ p ~ q ~ p ~ q T T F F F T F F T T F T T F F F F T T T 6

7 Use a truth table to show that p q and ~ p q are equivalent. Then use the result to write a statement that is equivalent to the statement shown. 24) If the garden is not watered every day, the flowers wilt. 24) A) p q p q ~ p ~ p q T T T F T T F F F F F T T T T F F T T T The flowers do not wilt if and only if the garden is not watered every day. B) p q p q ~ p ~ p q T T T F T T F F F F F T T T T F F T T T Either the garden is not watered every day, or the flowers don't wilt. C) p q p q ~ p ~ p q T T T F T T F F F F F T T T T F F T T T The flowers wilt if the garden is not watered every day. D) p q p q ~ p ~ p q T T T F T T F F F F F T T T T F F T T T Either the garden is watered every day, or the flowers wilt. Write the equivalent contrapositive of the statement. 25) If the news report is accurate, then people are generally happy. 25) A) If people are generally not happy, then the news report is not accurate. B) If the news report is not accurate, then it is misleading. C) If the news report is not accurate, then news report not happy. D) If people are generally not happy, then the news report is accurate. 7

8 Write the nonequivalent converse and inverse of the statement. 26) If you are sleeping, then you are not dancing. 26) A) converse: If you are not dancing, then you are sleeping. inverse: If you are not sleeping, then you are dancing B) converse: If you are not sleeping, then you are dancing inverse: If you are not dancing, then you are sleeping. C) converse: If you are not dancing, then you are sleeping. inverse: If you are sleeping, then you are not dancing D) converse: If you are dancing, then you are not sleeping. inverse: If you are not sleeping, then you are dancing Write the negation of the conditional statement. 27) If it is black, then it is not a cornflower. 27) A) It is black and it is not a cornflower. B) It is not black and it is not a cornflower. C) It is black and it is a cornflower. D) It is not black and it is a cornflower. Use De Morgan's laws to write a statement that is equivalent to the statement given. 28) It is not true that Ireland and Utah are both cities. 28) A) If Ireland is a city, then Utah is not a city. B) Ireland is not a city and Utah is not a city. C) It is true that Ireland and Utah are both cities. D) Ireland is not a city or Utah is not a city. Use De Morgan's laws to write a negation of the statement. 29) Cats are lazy or dogs aren't friendly. 29) A) Cats are lazy and dogs are friendly. B) Cats aren't lazy or dogs are friendly. C) Cats aren't lazy and dogs are friendly. D) Cats aren't lazy or dogs aren't friendly. 8

9 Use a truth table to determine whether the symbolic form of the argument is valid or invalid. 30) p q 30) ~ p ~ q A) p q p q ~ p (p q) ~ p ~ q [ (p q) ~ p ] ~ q T T T F F F T T F F F F T T F T F T F F T F F F T F T T The argument is valid. B) p q p q ~ p (p q) ~ p ~ q [ (p q) ~ p ] ~ q T T T F T F T T F F F F T T F T F T T F T F F F T T T T The argument is valid. C) p q p q ~ p (p q) ~ p ~ q [ (p q) ~ p ] ~ q T T T F F F T T F F F F T T F T T T T F F F F T T T T T The argument is invalid. D) p q p q ~ p (p q) ~ p ~ q [ (p q) ~ p ] ~ q T T T F F F T T F F F T T T F T T T T F F F F T T T T T The argument is invalid. Find the measure of the complement of the angle. 31) Find the complement of 9. 31) A) 261 B) 351 C) 81 D) 171 9

10 Find the measures of angles 1, 2, and 3. 32) 32) 52 A) 1 = 128 ; 2 = 52 ; 3 = 128 B) 1 = 38 ; 2 = 90 ; 3 = 38 C) 1 = 38 ; 2 = 104 ; 3 = 38 D) 1 = 38 ; 2 = 90 ; 3 = 52 Find the measure of angle A for the triangle shown. 33) 33) A) 43 B) 223 C) 17 D) 60 Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x. 34) 34) 15 m 3 m 5 m 12 m 4 m A) 5 m B) 3 m C) 12 m D) 9 m Use the Pythagorean Theorem to find the missing length in the right triangle. Use a calculator to find square roots, rounding, if necessary, to the nearest tenth. 35) 35) 6 m 10 m b A) 7 m B) 10 m C) 8 m D) 9 m Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 36) Triangle 36) 8 yd 4 yd 9 yd A) 20 yd B) 17 yd C) 18 yd D) 21 yd 10

11 Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 37) 5 in. 6 in. 37) 5 in. 20 in. 15 in. A) 75 in. B) 91 in. C) 60 in. D) 80 in. Solve the problem. 38) Find the sum of the measures of the angles of a 7-sided polygon. 38) A) 900 B) 180 C) 720 D) 1260 Use formulas to find the area of the figure. 39) 4 mi 39) 1.5 mi 1.3 mi 1.5 mi 4 mi A) 5.5 sq. mi B) 52 sq. mi C) 5.2 sq. mi D) 6 sq. mi Find the area of the figure. 40) 18 yd 40) 4 yd 13 yd 4 yd A) 88 yd2 B) 84 yd2 C) 93 yd2 D) 124yd2 Solve the problem. Round all circumference and area calculations to the nearest whole number. 41) One pizza shop sells a tasty large pizza with a 12-inch diameter for $ Another pizza shop 41) sells a tasty medium pizza with a 8-inch diameter for $5.00. Which is the better buy? A) The large pizza is the better buy. B) The two pizzas are equally good buys. C) The medium pizza is the better buy. 11

12 Find the volume of the figure. If necessary, round the answer to the nearest whole number. 42) 42) 7 cm 14 cm A) 308 cm3 B) 539 cm3 C) 154 cm3 D) 2154 cm3 43) 43) 6 in. A) 151 in.3 B) 509 in.3 C) 904 in.3 D) 113 in.3 Find the surface area of the figure. 44) 44) 3 m 4 m 7 m A) 84 m2 B) 168 m2 C) 61 m2 D) 122 m2 Use the given right triangle to find the trigonometric function. 45) sin B 45) A) 3 5 B) 5 3 C) 4 3 D)

13 46) cos B 46) A) 5 12 B) C) 5 13 D) Find the measure of the side of the right triangle whose length is designated by the lowercase letter. Round your answer to the nearest whole number. 47) 47) 40 b = 180 cm a A) 165 cm B) 147 cm C) 151 cm D) 160 cm Use the inverse trigonometric keys on a calculator to find the measure of angle A, rounded to the nearest whole degree. 48) 48) 34 cm 27 cm A) 34 B) 35 C) 37 D) 36 Solve the problem. 49) At a certain time of day, the angle of elevation of the sun is 62. To the nearest foot, find the height 49) of a pole whose shadow at that time is 14 feet long ft A) 28 feet B) 30 feet C) 26 feet D) 7 feet 13

14 50) For one instant, a hot air balloon is 580 feet above the ocean. The figure shows that the angle of 50) depression from the balloon to point P is 39. How far, to the nearest foot, is point P to the point directly below the balloon on the surface of the water? 580 ft 39 A) 18,160 feet B) 523 feet C) 496 feet D) 443 feet 14