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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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 $n (U) = 15$

The total number of lines having verb be $n (V) = 10$

The total number of lines having verb be $n (A) = 10$

The total number of lines having both verb and adjective be $n (V \cap A) = 7$ .

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

$\begin{matrix} n (V - A) = n (V) - n (V \cap A) \\ = 10 - 7 \\ = 3 \end{matrix}$

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

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