If A ⊆ U, |U| = 9, and |A′| = 4, how many proper subsets does A have?
Advertisement
Answer and explanation
Correct answer: 31
Because A′ contains the elements of U that are not in A, |A| = |U| − |A′| = 9 − 4 = 5. A set with n elements has 2ⁿ total subsets, so A has 2⁵ = 32 subsets. Proper subsets exclude the set itself, while still including the empty set; therefore, the number of proper subsets is 32 − 1 = 31. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
Because A′ contains the elements of U that are not in A, |A| = |U| − |A′| = 9 − 4 = 5. A set with n elements has 2ⁿ total subsets, so A has 2⁵ = 32 subsets. Proper subsets exclude the set itself, while still including the empty set; therefore, the number of proper subsets is 32 − 1 = 31. Hence, option B 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