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The management of a hotel conducted a survey of 7,000 guests and their tipping habits. The results are in the following Venn diagram, with W representing those who tipped the wait staff, M representing those who tipped room-cleaning staff, and L representing those who tipped the concierge.

(a) How many people tipped exactly one service?

people

(b) How many people tipped all three services?

people

(d) How many people did not tip any of the services?

people

for each question part only changes if you submit or change the answer.

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1. AUFQR1 2.1.053.–/4 POINTS MY NOTES ASK YOUR TEACHER

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A new drug to control blood pressure was given to 1,000 patients. Another 1,000 patients were given a placebo. The result showed that 750 of the patients receiving the new drug had a decrease in blood pressure. For the group that received the placebo, 238 had a decrease in blood pressure. The results are shown in the following Venn diagram.

(a) Use the Venn diagram to complete the following table.

Reduced Blood Pressure No Blood Pressure Reduction

Received New Drug

Received Placebo

(b) How many false negatives occurred?

There were cases in which there was ---Select--- and the patient received the ---Select--- .

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250 750 238

762

2. AUFQR1 2.1.058.–/8 POINTS MY NOTES ASK YOUR TEACHER

A survey found that 44 people liked chocolate, 26 people like peanut butter, and 16 people liked both. How many people were in the survey? (See Example 8 in this section.)

people

A test for a performance-enhancing drug is given to 200 athletes. The results are shown in the following Venn diagram. (See Example 11 in this section.)

Using the Venn diagram, complete the following table.

Positive Test Negative Test

Athlete Has Banned Drug

Athlete Does Not Have Banned Drug

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15 20 11

154

3. AUFQR1 2.1.P.008.–/1 POINTS MY NOTES ASK YOUR TEACHER

4. AUFQR1 2.1.P.011.–/4 POINTS MY NOTES ASK YOUR TEACHER

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Write the negation of the statement. Start the negation with the word "Some," "No," or "All."

All classic movies were first produced in black and white.

Some classic movies were not first produced in black and white.

All classic movies were not first produced in black and white.

Some classic movies were first produced in black and white.

No classic movies were not first produced in black and white.

No classic movies were first produced in black and white.

5. AUFQR1 2.2.003.–/1 POINTS MY NOTES ASK YOUR TEACHER

Use an Euler diagram to determine whether the argument is valid or invalid.

Choose the Euler diagram that shows whether the argument is valid or invalid.

All frogs are poetical. Kermit is a frog.

∴ Kermit is poetical.

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6. AUFQR1 2.2.009.–/2 POINTS MY NOTES ASK YOUR TEACHER

Is the argument valid or invalid?

valid

invalid

Use an Euler diagram to determine whether the argument is valid or invalid.

Choose the Euler diagram that shows whether the argument is valid or invalid.

All men behave badly. Some hockey players behave badly.

∴ Some hockey players are men.

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7. AUFQR1 2.2.017.–/2 POINTS MY NOTES ASK YOUR TEACHER

Is the argument valid or invalid?

valid

invalid

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Use an Euler diagram to determine whether the argument is valid or invalid.

Choose the Euler diagram that shows whether the argument is valid or invalid.

No mathematics test is fun. All fun things are worth your time.

∴ No mathematics test is worth your time.

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8. AUFQR1 2.2.021.–/2 POINTS MY NOTES ASK YOUR TEACHER

Is the argument valid or invalid?

valid

invalid

ℹ

Use an Euler diagram to determine whether the argument is valid or invalid.

Choose the Euler diagram that shows whether the argument is valid or invalid.

Is the argument valid or invalid?

valid

invalid

All aerobics classes are fun. Jan's class is fun.

∴ Jan's class is an aerobics class.

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9. AUFQR1 2.2.027.–/2 POINTS MY NOTES ASK YOUR TEACHER

Examine the following three premises.

1. All people who have an Xbox play video games. 2. All people who play video games enjoy life. 3. Some mathematics professors enjoy life.

Now consider each of the following six conclusions. For each conclusion, determine whether the argument formed by the three premises and the conclusion is valid or invalid.

(a) ∴ Some mathematics professors have an Xbox.

valid

invalid

(b) ∴ Some mathematics professors play video games.

valid

invalid

valid

invalid

(d) ∴ Mathematics professors never play video games.

valid

invalid

(e) ∴ All people who have an Xbox enjoy life.

valid

invalid

(f) ∴ Some people who enjoy life are mathematics professors.

valid

invalid

10. AUFQR1 2.2.035.–/6 POINTS MY NOTES ASK YOUR TEACHER

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