Please write answers in a way that is easy to follow for someone very confused 114. If A and B are sets within some universal set, then prove, using properties of sets, that thefollowing equality holds.сJ%|A'U B|-|A'n B'| = |B|MacBook ProSearch or type URL&*►

We need to prove that for some sets within a universal set.Let be the universal set.We know that:

Answered: If A and B are sets within some…

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

Please write answers in a way that is easy to follow for someone very confused

11
4. If A and B are sets within some universal set, then prove, using properties of sets, that the
following equality holds.
с
J
%
|A'U B|-|A'n B'| = |B|
MacBook Pro
Search or type URL
&
*
►

Expert Solution

Step 1: Introduction

We need to prove that $open vertical bar A apostrophe union B close vertical bar minus open vertical bar A apostrophe intersection B apostrophe close vertical bar equals open vertical bar B close vertical bar$ for some sets $A comma B$ within a universal set.

Let $U$ be the universal set.

We know that:

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