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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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A study was done to determine the efficacy of three different drugs— AB, and C — in relieving headache pain. Ove the period covered by the study, 50 subjects were given the change to use all three drugs. The following results were obtained:

21 reported relief from drug A
21 reported relief from drug B
31 reported relief from drug C
9 reported relief from both drugs A and B
14 reported relief from both drugs A and C
15 reported relief from both drugs B and C
41 reported relief from at least one of the drugs.

Note that some of the 21 subjects who reported relief from drug A may also have reported relief from drugs B or C. A similar occurrence may be true for the other data.
a. How many people got relief from none of the drugs?
b. How many people got relief from all three drugs?
c. Let A be the set of all subjects who got relief from drug A, B the set of all subjects who got relief from drug B, and C the set of all numbers for all eight regions of the following diagram.
Chapter 9.3, Problem 34ES, A study was done to determine the efficacy of three different drugs— A, B, and C — in relieving
d. How many subjects got relief from A only?

To determine

(a)

The number of people who did not get relief from any type of drug.

Explanation

Given information:

In a study to examine the ability to relieving of three type of drugs A,B and C for headache.

50 patients who got suffered from headache were given the chance to test the drug.

The result was summarized as follows.

21 reported relief from drug A.

21 reported relief from drug B.

31 reported relief from drug C.

9 reported relief from both drugs A and B.

14 reported relief from both drugs A and C.

15 reported relief from both drugs B and C.

41 reported relief from at least one of the drugs

To determine

(b)

The count of the people who got relief from all three drugs.

To determine

(c)

To construct a Venn diagram for the given scenario considering three sets A,Band C regarding the three drugs.

To determine

(d)

To find:

The number of patients who have got reliefonly from A.

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