MP Board · Class 11 · Mathematics · SetsIf $A = \{1, 2, 3\}$, what is the power set $P(A)$?
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Total Attempts: 4
Accuracy Rate: 50%
Step-by-Step Solution
The power set of a set $A$ is the set of all subsets of $A$. For $A = {1, 2, 3}$, the subsets are $\emptyset, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}$. Thus, $P(A)$ contains $2^3 = 8$ elements.
Detailed Options Breakdown
Option : \{\emptyset, \{1\}, \{2\}, \{3\}, \{1, 2\}, \{1, 3\}, \{2, 3\}, \{1, 2, 3\}\} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: \{\{1\}, \{2\}, \{3\}, \{1, 2, 3\}\}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sets.
Option 2: \{\emptyset, \{1, 2, 3\}\}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sets.
Option 3: \{1, 2, 3, \{1, 2\}, \{2, 3\}, \{1, 3\}\}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sets.
💡 Study Guide: This question tests core syllabus concepts from Sets. For formulas, key summaries, and mock exam reference guides, read the full Sets Revision Notes.