Please write answers in a way that is easy to follow for someone very confused . If you can’t solve all parts please solve c and d #3с$43. A mathematician was attempting to sort his chalk into three categories. Of the 48 bits ofchalk he had collected, 24 were too small to use, 17 were very pointy, 6 produced dottedlines, 20 were too small and not very pointy, 28 were too small or produced dotted lines, 22were very pointy or produced dotted lines, and 19 were too small to use and not verypointy and did not produce dotted lines.(a) Draw, and fully label, a Venn diagram representing the given information.(b) How many pieces of chalk were too small to use or very pointy or produced dottedlines?(c) How many pieces of chalk were neither too small nor produced dotted lines?(d) How many pieces of chalk were neither too small nor very pointed nor produced dottedlines?MacBook ProG Search or type URL%56V&7☆*0089)0

Let denote the chalk too small to use. denote very pointy and denote produced dotted…

Answered: A mathematician was attempting to sort…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Please write answers in a way that is easy to follow for someone very confused . If you can’t solve all parts please solve c and d

#
3
с
$
4
3. A mathematician was attempting to sort his chalk into three categories. Of the 48 bits of
chalk he had collected, 24 were too small to use, 17 were very pointy, 6 produced dotted
lines, 20 were too small and not very pointy, 28 were too small or produced dotted lines, 22
were very pointy or produced dotted lines, and 19 were too small to use and not very
pointy and did not produce dotted lines.
(a) Draw, and fully label, a Venn diagram representing the given information.
(b) How many pieces of chalk were too small to use or very pointy or produced dotted
lines?
(c) How many pieces of chalk were neither too small nor produced dotted lines?
(d) How many pieces of chalk were neither too small nor very pointed nor produced dotted
lines?
MacBook Pro
G Search or type URL
%
5
6
V
&
7
☆
*00
8
9
)
0

Expert Solution

Step 1: Introduction

Let $S$ denote the chalk too small to use.

$P$ denote very pointy and $D$ denote produced dotted line.

Therefore using given information, we have:
$table row cell open vertical bar text Universal end text close vertical bar end cell equals 48 row cell open vertical bar S close vertical bar end cell equals 24 row cell open vertical bar P close vertical bar end cell equals 17 row cell open vertical bar D close vertical bar end cell equals 6 row cell open vertical bar S intersection P apostrophe close vertical bar end cell equals 20 row cell open vertical bar S union D close vertical bar end cell equals 28 row cell open vertical bar P union D close vertical bar end cell equals 22 row cell open vertical bar S intersection P apostrophe intersection D apostrophe close vertical bar end cell equals 19 end table$

We know following identity of sets:

$table row cell open vertical bar A union B close vertical bar end cell equals cell open vertical bar A close vertical bar plus open vertical bar B close vertical bar minus open vertical bar A intersection B close vertical bar end cell row cell open vertical bar A intersection B apostrophe close vertical bar end cell equals cell open vertical bar A close vertical bar minus open vertical bar A intersection B close vertical bar end cell row cell open vertical bar A intersection B apostrophe intersection C apostrophe close vertical bar end cell equals cell open vertical bar A close vertical bar minus open vertical bar A intersection B close vertical bar minus open vertical bar A intersection C close vertical bar plus open vertical bar A intersection B intersection C close vertical bar end cell end table$