If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is the value of |P(A ∩ B)|, where P denotes the power set?
Answer and explanation
Correct answer: 4
The governing concept is the power-set cardinality rule: a finite set with n elements has 2ⁿ subsets. First find the intersection: A ∩ B = {3, 4}, so it contains n = 2 elements. Therefore, |P(A ∩ B)| = 2² = 4. Option B is correct. The values 2 and 8 result from using the wrong exponent, while 16 would correspond to four elements.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is the power-set cardinality rule: a finite set with n elements has 2ⁿ subsets. First find the intersection: A ∩ B = {3, 4}, so it contains n = 2 elements. Therefore, |P(A ∩ B)| = 2² = 4. Option B is correct. The values 2 and 8 result from using the wrong exponent, while 16 would correspond to four elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
