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Chapter 1: Problem 1

Write the following sets by listing their elements between braces. $$ \mathscr{P}(\\{\\{a, b\\},\\{c\\}\\}) $$

Short Answer

Expert verified
The power set is: \(\{\{\}, \{\{a, b\}\}, \{\{c\}\}, \{\{a, b\}, \{c\}\}\}\).

Step by step solution

01

Identify The Sets

Firstly, identify the sets given in the problem. Here, there are two sets: \(\{a, b\}\) and \(\{c\}\). The power set problem is defined on these two sets.
02

Identify the Subsets

Next, identify all the subsets that can be formed from the given sets. By definition, a power set includes all possible subsets. So, the subsets are: the empty set \(\{\}\), the individual sets themselves (\(\{a, b\}\) and \(\{c\}\)), and both sets combined (\(\{a, b\}, \{c\}\)).
03

List the Elements

Now, list out all the subsets mentioned in step 2 as elements of the power set. Therefore, the power set is: \(\{\{\}, \{\{a, b\}\}, \{\{c\}\}, \{\{a, b\}, \{c\}\}\}\).

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Most popular questions from this chapter

Sketch these Cartesian products on the \(x-y\) plane \(\mathbb{R}^{2}\) (or \(\mathbb{R}^{3}\) for the last two). $$ [0,1] \times\\{1\\} $$

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