# Stocks Exercises 49–54 are based on the following table, which shows the stock market performance of 40 industries from five sectors of the U.S. economy as of noon on September 11, 2015. 9 (Take S to be the set of all 40 industries represented in the table.) Increased ( X ) Decreased ( Y ) Unchanged ( Z ) Totals Financials ( F ) 3 4 1 8 Manufacturing ( M ) 8 3 3 14 Information Technology ( T ) 6 1 0 7 Health Care ( H ) 4 1 1 6 Utilities ( U ) 3 1 1 5 Totals 24 10 6 40 Compute n ( T ∩ Y ) n ( Y ) . What does the answer represent?

### Finite Mathematics

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337280426

### Finite Mathematics

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337280426

#### Solutions

Chapter
Section
Chapter 6.2, Problem 53E
Textbook Problem

## Stocks Exercises 49–54 are based on the following table, which shows the stock market performance of 40 industries from five sectors of the U.S. economy as of noon on September 11, 2015.9 (Take S to be the set of all 40 industries represented in the table.) Increased ( X ) Decreased ( Y ) Unchanged ( Z ) Totals Financials ( F ) 3 4 1 8 Manufacturing ( M ) 8 3 3 14 Information Technology ( T ) 6 1 0 7 Health Care ( H ) 4 1 1 6 Utilities ( U ) 3 1 1 5 Totals 24 10 6 40 Compute n ( T ∩ Y ) n ( Y ) . What does the answer represent?

Expert Solution
To determine

To calculate: The value of n(TY)n(Y) and its representation using the table given below:

 Increased (X) Decreased (Y) Unchanged (Z) Total Financials (F) 3 4 1 8 Manufacturing (M) 8 3 3 14 Information Technology (T) 6 1 0 7 Health Care (H) 4 1 1 6 Utilities (U) 3 1 1 5 Total 24 10 6 40

### Explanation of Solution

Given Information:

The following table shows the stock market performance of 40 industries from five sectors of the U.S economy as of noon on September 11, 2015, with S as the set of all 40 industries,

 Increased (X) Decreased (Y) Unchanged (Z) Total Financials (F) 3 4 1 8 Manufacturing (M) 8 3 3 14 Information Technology (T) 6 1 0 7 Health Care (H) 4 1 1 6 Utilities (U) 3 1 1 5 Total 24 10 6 40

Formula used:

If A is a finite set, then its cardinality is

n(A)=number of elements in A

Calculation:

Consider the provided table,

 Increased (X) Decreased (Y) Unchanged (Z) Total Financials (F) 3 4 1 8 Manufacturing (M) 8 3 3 14 Information Technology (T) 6 1 0 7 Health Care (H) 4 1 1 6 Utilities (U) 3 1 1 5 Total 24 10 6 40

The set X represents the increased stock market performance. The set Y represents the decreased stock market performance. The set Z represents the unchanged stock market performance. The set F represents the Financials stock market performance. The set M represents the Manufacturing stock market performance. The set T represents the Information Technology stock market performance. The set H represents the Health Care stock market performance. The set U represents the Utilities stock market performance.

Reconstruct the table using symbols for sets,

 Increased (X) Decreased (Y) Unchanged (Z) Total Financials (F) n(X∩F) n(Y∩F) n(Z∩F) n(F) Manufacturing (M) n(X∩M) n(Y∩M

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