If U = {1,2,3,4,5} and A = {1,2}, why is P(A') ⊆ P(U) true?
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Answer and explanation
Correct answer: Because A' ⊆ U
The complement A' is defined relative to U, so A' = {3,4,5}. Every element of A' is therefore an element of U, which means A' ⊆ U. Whenever one set is a subset of another, every subset of the smaller set is also a subset of the larger set. Consequently P(A') ⊆ P(U), making option A correct.
Frequently asked questions
What is the correct answer to this question?
Because A' ⊆ U
Why is this the correct answer?
The complement A' is defined relative to U, so A' = {3,4,5}. Every element of A' is therefore an element of U, which means A' ⊆ U. Whenever one set is a subset of another, every subset of the smaller set is also a subset of the larger set. Consequently P(A') ⊆ P(U), making option A correct.
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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