1 Answer

Petronila · Answer 1 · 2020-02-25T02:15:32+0000

$Z=\{a,c,\{a,b\}\}$

$\boxedZ$ (treat
$\{a,b\}$ as one element of
)

The power set of
is

$\boxed{2^Z=\bigg\{\{\},\{a\},\{c\},\big\{\{a,b\}\big\},\{a,c\},\big\{a,\{a,b\}\big\},\big\{c,\{a,b\}\big\},\big\{a,c,\{a,b\}\big\}\bigg\}}$

1.
$\{a,c\}\subseteq Z$ is true because both
$a\in Z$ and
$c\in Z$ .

2.
$a\in Z$ is true.

3.
$\{c\}\subseteq Z$ is true (same reason as part 1).

4.
$\{c\}\in Z$ is false because
does not contain the set
$\{c\}$ , rather just the element
itself.

5.
$b\in Z$ is false because the element
on its own simply is not in
. That
$b\in\{a,b\}$ does not mean
$b\in Z$ , but that
belongs to a subset of
.

6.
$\{a,b\}\in Z$ is true.

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