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One of Shakespeare's sonnets has a verb in 10 of its 15 lines, an adjective in 10 lines, and both in 7 lines. How many lines have a verb but no adjective? How many lines have an adjective but no verb? How many have neither an adjective nor a verb?

One of Shakespeare's sonnets has a verb in 10 of its 15 lines, an adjective in 10 lines, and both in 7 lines. How many lines have a verb but no adjective? How many lines have an adjective but no verb? How many have neither an adjective nor a verb?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
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One of Shakespeare's sonnets has a verb in 10 of its 15 lines, an adjective in 10 lines, and both in 7 lines. How many lines have a verb but no adjective? How many lines have an adjective but no verb? How many have neither an adjective nor a verb?
Transcribed Image Text:One of Shakespeare's sonnets has a verb in 10 of its 15 lines, an adjective in 10 lines, and both in 7 lines. How many lines have a verb but no adjective? How many lines have an adjective but no verb? How many have neither an adjective nor a verb?
Expert Solution
Step 1

Let the total number of lines be nU=15

The total number of lines having verb be nV=10

The total number of lines having verb be nA=10

The total number of lines having both verb and adjective be nV∩A=7.

First find the number of lines have a verb but no adjective.

Hence, the number of lines have a verb but no adjective is given by

nV−A=nV−nV∩A=10−7=3

Hence, the number of lines have a verb but no adjective is 3.

 

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