If A = ∅, how many subsets does A have?
Answer and explanation
Correct answer: 1
The empty set has zero elements, so |A| = 0. A set with n elements has exactly 2^n subsets, because each element may either be included or excluded from a subset. Thus the empty set has 2^0 = 1 subset. That single subset is the empty set itself. It is incorrect to say zero subsets, because every set contains itself as a subset; two subsets would apply to a one-element set.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The empty set has zero elements, so |A| = 0. A set with n elements has exactly 2^n subsets, because each element may either be included or excluded from a subset. Thus the empty set has 2^0 = 1 subset. That single subset is the empty set itself. It is incorrect to say zero subsets, because every set contains itself as a subset; two subsets would apply to a one-element set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
