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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 18

If A = {a, b, c, d} and B = {c, d, e}, how many elements does P(A ∩ B) contain?

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Answer and explanation

Correct answer: 4

First determine the intersection. The elements common to A = {a, b, c, d} and B = {c, d, e} are c and d, so A ∩ B = {c, d} and has 2 elements. A set with n elements has 2ⁿ subsets in its power set. Therefore, P(A ∩ B) has 2² = 4 elements, making option A correct.

Tags

setspower-setintersectioncardinalityOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

First determine the intersection. The elements common to A = {a, b, c, d} and B = {c, d, e} are c and d, so A ∩ B = {c, d} and has 2 elements. A set with n elements has 2ⁿ subsets in its power set. Therefore, P(A ∩ B) has 2² = 4 elements, making option A correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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