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If P(A)⊆P(U), which statement is definitely true?
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Answer and explanation
Correct answer: A⊆U
The set A is always a member of its own power set because A⊆A. Since P(A)⊆P(U), it follows that A∈P(U). By the definition of a power set, A∈P(U) means A⊆U. The other choices are not forced: A may be a proper subset of U, so option A is the only definitely true statement.
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What is the correct answer to this question?
A⊆U
Why is this the correct answer?
The set A is always a member of its own power set because A⊆A. Since P(A)⊆P(U), it follows that A∈P(U). By the definition of a power set, A∈P(U) means A⊆U. The other choices are not forced: A may be a proper subset of U, so option A is the only definitely true statement.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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