If A = {1,2} and B = {3,4}, then what is P(A) ∩ P(B)?
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Answer and explanation
Correct answer: {∅}
P(A) = {∅, {1}, {2}, {1,2}} and P(B) = {∅, {3}, {4}, {3,4}}. The only common subset is ∅, because no nonempty subset can simultaneously contain only elements from A and only elements from B when A and B are disjoint. Therefore, their intersection is the set containing ∅, namely {∅}.
Frequently asked questions
What is the correct answer to this question?
{∅}
Why is this the correct answer?
P(A) = {∅, {1}, {2}, {1,2}} and P(B) = {∅, {3}, {4}, {3,4}}. The only common subset is ∅, because no nonempty subset can simultaneously contain only elements from A and only elements from B when A and B are disjoint. Therefore, their intersection is the set containing ∅, namely {∅}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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