Write out the indicated sets by listing their elements between braces

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The expression represents a set defined using set-builder notation. It describes the set of all subsets \( X \) of the set \(\{1, 2, 3\}\) such that the number 2 is an element of \( X \).

- \(\mathcal{P}(\{1, 2, 3\})\) denotes the power set of \(\{1, 2, 3\}\), which is the set of all possible subsets of \(\{1, 2, 3\}\).
- \(X \in \mathcal{P}(\{1, 2, 3\})\) indicates that \(X\) is a subset of \(\{1, 2, 3\}\).
- \(2 \in X\) specifies that the number 2 must be an element of these subsets.

Therefore, the set consists of subsets like \(\{2\}\), \(\{1, 2\}\), \(\{2, 3\}\), and \(\{1, 2, 3\}\).
Transcribed Image Text:The expression represents a set defined using set-builder notation. It describes the set of all subsets \( X \) of the set \(\{1, 2, 3\}\) such that the number 2 is an element of \( X \). - \(\mathcal{P}(\{1, 2, 3\})\) denotes the power set of \(\{1, 2, 3\}\), which is the set of all possible subsets of \(\{1, 2, 3\}\). - \(X \in \mathcal{P}(\{1, 2, 3\})\) indicates that \(X\) is a subset of \(\{1, 2, 3\}\). - \(2 \in X\) specifies that the number 2 must be an element of these subsets. Therefore, the set consists of subsets like \(\{2\}\), \(\{1, 2\}\), \(\{2, 3\}\), and \(\{1, 2, 3\}\).
**Instruction:**

Write out the indicated sets by listing their elements between braces.
Transcribed Image Text:**Instruction:** Write out the indicated sets by listing their elements between braces.
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