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Web Searches In November 2011 a search using the web search engine Bing for “tea party” yielded 58.0 million websites containing that phrase. A search for “coffee party” yielded 0.6 million sites. A search for sites containing both phrases yielded 0.1 million sites. 5 How many websites contained either “tea party” or “coffee party” or both? [ HINT: See Example 1.]

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Finite Mathematics

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337280426
Chapter 6.2, Problem 32E
Textbook Problem
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Web Searches In November 2011 a search using the web search engine Bing for “tea party” yielded 58.0 million websites containing that phrase. A search for “coffee party” yielded 0.6 million sites. A search for sites containing both phrases yielded 0.1 million sites.5 How many websites contained either “tea party” or “coffee party” or both?

[HINT: See Example 1.]

To determine

To calculate: The number of websites that contained either “tea-party” or “coffee-party” or both if a search using the web search engine Bing in November 2011 for “tea-party” resulted in 58.0 million websites and a search for “coffee-party” resulted in 0.6 million sites. Also, a search for sites containing both words resulted in 0.1 million sites.

Explanation of Solution

Given Information:

A search using the web search engine Bing in November 2011 for “tea-party” resulted in 58.0 million websites and a search for “coffee-party” resulted in 0.6 million sites. Also, a search for sites containing both words resulted in 0.1 million sites.

Formula used:

For union of sets X, with number of elements n(X), and set Y, with number of elements n(Y),

n(XY)=n(X)+n(Y)n(XY)

If A is a finite set, then its cardinality is

n(A)=number of elements in A

Calculation:

Consider the set of websites containing the word “tea-party” to be X and the set of websites containing the word “coffee-party” to be Y.

A search using the web search engine Bing for “tea-party” yielded 58.0 million websites. Thus, there are 58.0 million websites in the set, X.

This can be represented by,

n(X)=58.0

A search using the web search engine Bing for “coffee-party” yielded 0.6 million websites. Thus, there are 0.6 million websites in the set, Y

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