If |P(A)| = 32 and |P(B)| = 8, what is |P(A × B)|?
Advertisement
Answer and explanation
Correct answer: 2^15
For any finite set X, |P(X)| = 2^|X|. From |P(A)| = 32 = 2^5, we get |A| = 5. Similarly, |P(B)| = 8 = 2^3, so |B| = 3. The Cartesian product A × B therefore has |A||B| = 5 × 3 = 15 ordered pairs. Its power set consequently has 2^15 elements. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
2^15
Why is this the correct answer?
For any finite set X, |P(X)| = 2^|X|. From |P(A)| = 32 = 2^5, we get |A| = 5. Similarly, |P(B)| = 8 = 2^3, so |B| = 3. The Cartesian product A × B therefore has |A||B| = 5 × 3 = 15 ordered pairs. Its power set consequently has 2^15 elements. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement