If A ⊆ B ⊆ U, |U| = 9, |B| = 6, and |A| = 4, what is |P(B − A)| + |P(U − B)|?
Answer and explanation
Correct answer: 12
Because A is a subset of B, the elements in B − A are obtained by subtracting the cardinality of A from that of B: |B − A| = 6 − 4 = 2. Also, since B is a subset of U, |U − B| = 9 − 6 = 3. A two-element set has 2^2 = 4 subsets, while a three-element set has 2^3 = 8 subsets. Hence the required sum is 4 + 8 = 12, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Because A is a subset of B, the elements in B − A are obtained by subtracting the cardinality of A from that of B: |B − A| = 6 − 4 = 2. Also, since B is a subset of U, |U − B| = 9 − 6 = 3. A two-element set has 2^2 = 4 subsets, while a three-element set has 2^3 = 8 subsets. Hence the required sum is 4 + 8 = 12, so 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.
