If A = {∅, {∅}}, how many elements does its power set P(A) contain?
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Answer and explanation
Correct answer: 4
The set A has two distinct elements: ∅ and {∅}. The empty set ∅ and the singleton set {∅} are different objects, even though one contains the other. A set with n elements has 2^n subsets, because every element can independently be selected or not selected. Therefore |A| = 2 and |P(A)| = 2^2 = 4. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The set A has two distinct elements: ∅ and {∅}. The empty set ∅ and the singleton set {∅} are different objects, even though one contains the other. A set with n elements has 2^n subsets, because every element can independently be selected or not selected. Therefore |A| = 2 and |P(A)| = 2^2 = 4. Thus option B is 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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