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Use a Venn diagram to decide if the statement is true or false

Question : Use a Venn diagram to decide if the statement is true or false : 2151573

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use a Venn diagram to decide if the statement is true or false.

1) A∩B' = (A'∪B)'

A) True

B) False

2) (A'∩B)' = A∩B'

A) True

B) False

3) (AB')' = A'∩B

A) True

B) False

4) (A'B)' = A'∩B

A) True

B) False

5) (A∩B)C = (AC)∩(AB)

A) True

B) False

6) B(A∩C) = (AB)∩(BC)

A) True

B) False

7) A'(B∩C) = (A'B)∩(A'C)

A) True

B) False

8) A(B∩C)' = (AB')∩(AC')

A) True

B) False

9) A(BC)' = (AB')∩(AC')

A) True

B) False

10) (AB)(AC) = A(BC)

A) True

B) False

Use a Venn diagram to answer the question.

11) At East Zone University (EZU) there are 651 students taking College Algebra or Calculus. 365 are taking College Algebra, 310 are taking Calculus, and 24 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus?

A) 627

B) 341

C) 317

D) 286

12) At East Zone University (EZU) there are 407 students taking College Algebra or Calculus. 191 are taking College Algebra, 252 are taking Calculus, and 36 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra?

A) 119

B) 216

C) 155

D) 371

13) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 500 responses with the following results:

150 were interested in an interview show and a documentary, but not reruns;

20 were interested in an interview show and reruns, but not a documentary;

70 were interested in reruns but not an interview show;

120 were interested in an interview show but not a documentary;

50 were interested in a documentary and reruns;

30 were interested in an interview show and reruns;

40 were interested in none of the three.

How many are interested in exactly one kind of show?

A) 220

B) 250

C) 230

D) 240

14) A survey of 280 families showed that

107 had a dog;

82 had a cat;

37 had a dog and a cat;

105 had neither a cat nor a dog, and in addition did not have a parakeet;

9 had a cat, a dog, and a parakeet.

How many had a parakeet only?

A) 38

B) 33

C) 23

D) 28

15) A survey of a group of 114 tourists was taken in St. Louis. The survey showed the following:

62 of the tourists plan to visit Gateway Arch;

48 plan to visit the zoo;

11 plan to visit the Art Museum and the zoo, but not the Gateway Arch;

12 plan to visit the Art Museum and the Gateway Arch, but not the zoo;

16 plan to visit the Gateway Arch and the zoo, but not the Art Museum;

8 plan to visit the Art Museum, the zoo, and the Gateway Arch;

15 plan to visit none of the three places.

How many plan to visit the Art Museum only?

A) 99

B) 35

C) 13

D) 61

16) A survey of 129 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information:

n(A) = 45; n(B) = 55; n(C) = 40;

n(A∩B) = 12; n(A∩C) = 15; n(B∩C) = 23;

n(A∩B∩C) = 2.

How many students were not taking any of these electives?

A) 47

B) 39

C) 10

D) 37

Find the number of elements in the indicated set by referring to the given table.

17) HA,

given the following table:

A) 1042

B) 2006

C) 543

D) 625

18) V∩W,

given the following table:

A) 230

B) 0

C) 364

D) 707

19) V∩(PW),

given the following table:

A) 161

B) 0

C) 363

D) 343

20) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set RF

A) 534

B) 555

C) 5

D) 550

21) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set O∩A'

A) 630

B) 25

C) 67

D) 1175

22) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set D(B∩O)

A) 747

B) 112

C) 0

D) 614

23) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set F∩(DR)

A) 1125

B) 1146

C) 0

D) 21

24) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set B(R'∩A)

A) 461

B) 988

C) 0

D) 440

25) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set O∩(C'E')

A) 65

B) 92

C) 525

D) 27

26) The table below shows the results of a poll taken in a U.S. city in which people are asked which candidate they intend to vote for in an upcoming presidential election.

Find the number of people in the set R'(AF)

A) 929

B) 1224

C) 812

D) 295

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