Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.2 Subsets - Exercise Set 2.2: 74

Answer

false $\{\emptyset\} \subseteq \{\emptyset, \{\emptyset\}\}$

Work Step by Step

$\{\emptyset\} \not\subseteq \{\emptyset, \{\emptyset\}\}$ This is incorrect, for it should say: $\{\emptyset\} \subseteq \{\emptyset, \{\emptyset\}\}$ Let's say: $A=\{\emptyset\}$ $B=\{\emptyset, \{\emptyset\}\}$ We can see that A's only element is an empty set ($\emptyset$). An empty set ($\emptyset$) is also an element of B. Therefore: $A\subseteq B$
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