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Chapter 3: Problem 33

List all the subsets of \(\mathrm{C}=\\{1,2\\}\).

Short Answer

Expert verified
The subsets of \(C = \{1, 2\}\) are: \(\emptyset, \{1\}, \{2\}, \{1, 2\}\).

Step by step solution

01

Identify the zero-element subset#

The empty set (or the set with no elements) is considered a subset of every set. In this case, we have one zero-element subset: \[\emptyset\]
02

Identify the one-element subsets#

We need to find all the subsets that contain only one element. Since there are two elements in set C, there will be two one-element subsets: \[\{1\}, \{2\}\]
03

Identify the two-element subset#

Lastly, we need to find the subset that contains both elements from the original set, which is simply the set itself, C: \[\{1, 2\}\]
04

List all subsets#

Now that we have found all the subsets for each case, we can list them all together. All the subsets of set C are: \[\emptyset, \{1\}, \{2\}, \{1, 2\}\]

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Most popular questions from this chapter

Let \(\mathrm{M}=\\{1,2\\}\) and \(\mathrm{N}=\\{\mathrm{p}, \mathrm{q}\\} .\) Find (a) \(\mathrm{M} \times \mathrm{N}\) (b) \(\mathrm{N} \times \mathrm{M}\), and (c) \(\mathrm{M} \times \mathrm{M}\)

If \(\mathrm{a}=\\{1,2,3,4,5)\) and \(\mathrm{b}=\\{2,3,4,5,6\\}\), find a n \(\mathrm{b}\).

$$ \begin{gathered} \mathrm{U}=\\{1,2,3,4,5,6,7,8,9,10\\}, \mathrm{P}=\\{2,4,6,8,10\\}, \\ \mathrm{Q}=\\{1,2,3,4,5\\} . \text { Find (a) } \mathrm{P} \text { and (b) } \mathrm{Q} \text { . } \end{gathered} $$

If \(\mathrm{a}=\\{1,2,3\\}\) and \(\mathrm{b}=\\{5,6\\}\), find \(\mathrm{a} \mathrm{x} \mathrm{b}\) and \(\mathrm{b} \times \mathrm{a}\).

If \(\mathrm{U}=\\{1,2,3,4,5\\}\) and \(\mathrm{A}=\\{2,4\\}\), find \(\mathrm{A}^{\prime}\)
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