(5) {1,2} C P({1, 2}).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Q3(5): Prove or Disprove

(5) \(\{1, 2\} \subseteq \mathcal{P}(\{1, 2\})\).

This mathematical expression states that the set \(\{1, 2\}\) is a subset of the power set of \(\{1, 2\}\). The power set of a set is the set of all subsets, including the empty set and the set itself. 

Detailed explanation:

- \(\{1, 2\}\) is a set containing the elements 1 and 2.
- \(\mathcal{P}(\{1, 2\})\) represents the power set of \(\{1, 2\}\), which is \(\{\emptyset, \{1\}, \{2\}, \{1, 2\}\}\).
- The expression \(\subseteq\) denotes that the set on the left is a subset of the set on the right, meaning all elements of the left set are contained within the right set.

In this context, \(\{1, 2\}\) is indeed included in \(\mathcal{P}(\{1, 2\})\) as one of the subsets.
Transcribed Image Text:(5) \(\{1, 2\} \subseteq \mathcal{P}(\{1, 2\})\). This mathematical expression states that the set \(\{1, 2\}\) is a subset of the power set of \(\{1, 2\}\). The power set of a set is the set of all subsets, including the empty set and the set itself. Detailed explanation: - \(\{1, 2\}\) is a set containing the elements 1 and 2. - \(\mathcal{P}(\{1, 2\})\) represents the power set of \(\{1, 2\}\), which is \(\{\emptyset, \{1\}, \{2\}, \{1, 2\}\}\). - The expression \(\subseteq\) denotes that the set on the left is a subset of the set on the right, meaning all elements of the left set are contained within the right set. In this context, \(\{1, 2\}\) is indeed included in \(\mathcal{P}(\{1, 2\})\) as one of the subsets.
Expert Solution
Step 1

Given  set is {1,2},

 we knew that power set of a given set is set of all subsets of the given set.

so power set of the given set is P({1,2}) = {{1} , {2} , {1,2},}

 

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