If U = {1,2,3,4,5,6,7,8,9,10,11}, A = {1,4,7,10}, and B = {2,4,6,8,10}, what is P(A ∩ B)?
Answer and explanation
Correct answer: {∅,{4},{10},{4,10}}
The common elements of A and B are 4 and 10, so A ∩ B = {4,10}. The power set contains every subset of this two-element set. These are the empty set, the two singleton subsets {4} and {10}, and the whole set {4,10}. Therefore P(A ∩ B) = {∅,{4},{10},{4,10}}, which is option C. The universal set U is not needed after finding the intersection.
Frequently asked questions
What is the correct answer to this question?
{∅,{4},{10},{4,10}}
Why is this the correct answer?
The common elements of A and B are 4 and 10, so A ∩ B = {4,10}. The power set contains every subset of this two-element set. These are the empty set, the two singleton subsets {4} and {10}, and the whole set {4,10}. Therefore P(A ∩ B) = {∅,{4},{10},{4,10}}, which is option C. The universal set U is not needed after finding the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
