Examples and Problems

Example 1.6

Example 1.6 gives a bunch of true statements with explanations. May emphasize the difference between the notations \(\in\) and \(\subseteq\). Let’s look at some of them.

1.6.1

\(1\not\subseteq\{1,\{1\}\}\)

1.6.3

\(\{1\}\in\{1,\{1\}\}\)

1.6.4

\(\{1\}\subseteq\{1,\{1\}\}\)

1.6.10

\(\emptyset\subseteq\mathbb{N}\)

1.6.12

\(\mathbb{N}\not\subseteq\{\mathbb{N}\}\)

Problem 1.3.9

Write out the elements of the set \(\{X:X\subseteq\{3,2,a\} \mathrm{\ and\ } |X|=2\}\)