$\backslash$section$*\{$Problem $2\}$

Describe explicitly in English the following sets, then find their cardinality.

$\backslash$begin$\{$enumerate$\}[$a$)]\%$ The enumerate environment produces a numbered list of items. The $[$a$)]$ ensures that the items are labelled with letters instead.

$\backslash$item $$\backslash$left$\backslash \{$x$\backslash$in $2^\{\backslash$mathbb$\{$Z$\}\}\backslash$mid $5\backslash$in x$\backslash$right$\backslash \}$$

$\backslash$item $$\backslash$left$\backslash \{$x$\backslash$in $2^\{\backslash$mathbb$\{$Z$\}\}\backslash$mid x$\backslash$subseteq$\backslash \{1,2,3\backslash \}\backslash$right$\backslash \}$$

$\backslash$item $$\backslash$left$\backslash \{$x$\backslash$in $2^\{\backslash$mathbb$\{$Z$\}\}\backslash$mid x$\backslash$subset$\backslash \{1,2,\backslash \{3,4\backslash \}\backslash \}\backslash$right$\backslash \}$$

$\backslash$item $$\backslash$left$\backslash \{$x$\backslash$in $2^\{\backslash$mathbb$\{$Z$\}\}\backslash$mid x$\backslash$in$\backslash \{1,2,\backslash \{3,4\backslash \}\backslash \}\backslash$right$\backslash \}$$

$\backslash$item $$\backslash$left$\backslash \{$x$\backslash$in $2^\{\backslash$mathbb$\{$Z$\}\}\backslash$mid y$\backslash$in x$\backslash$Longrightarrow y$=0\backslash$right$\backslash \}$$

$\backslash$end$\{$enumerate$\}$