If A = ∅, how many subsets does A have?
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Answer and explanation
Correct answer: 1
The number of subsets of a finite set with n elements is 2^n. The empty set has n = 0 elements, so it has 2^0 = 1 subset. That single subset is the empty set itself: P(∅) = {∅}. It is important not to confuse the number of elements in ∅, which is zero, with the number of its subsets, which is one.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The number of subsets of a finite set with n elements is 2^n. The empty set has n = 0 elements, so it has 2^0 = 1 subset. That single subset is the empty set itself: P(∅) = {∅}. It is important not to confuse the number of elements in ∅, which is zero, with the number of its subsets, which is one.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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