If A = {book, pen}, how many elements does P(A) have?
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Answer and explanation
Correct answer: 4
If a finite set has n elements, its power set has 2ⁿ elements because each original element can either be included or excluded from a subset. Here A has n = 2 elements, book and pen. Therefore |P(A)| = 2² = 4. The four subsets are ∅, {book}, {pen}, and {book, pen}.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
If a finite set has n elements, its power set has 2ⁿ elements because each original element can either be included or excluded from a subset. Here A has n = 2 elements, book and pen. Therefore |P(A)| = 2² = 4. The four subsets are ∅, {book}, {pen}, and {book, pen}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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