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Subjects
Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

Which statement is generally false?

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Answer and explanation

Correct answer: P(A) ∪ P(B) = P(A ∪ B)

The identity P(A) ∪ P(B) = P(A ∪ B) is generally false. The left side contains sets that are subsets entirely of A or entirely of B, whereas the right side also contains mixed subsets containing elements from both A and B. For example, if A={1} and B={2}, {1,2} belongs to P(A∪B) but not to P(A)∪P(B).

Tags

setspower-setfalse-identityunionPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

P(A) ∪ P(B) = P(A ∪ B)

Why is this the correct answer?

The identity P(A) ∪ P(B) = P(A ∪ B) is generally false. The left side contains sets that are subsets entirely of A or entirely of B, whereas the right side also contains mixed subsets containing elements from both A and B. For example, if A={1} and B={2}, {1,2} belongs to P(A∪B) but not to P(A)∪P(B).

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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