How many total subsets does the two-element set A = {a, b} have?
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Answer and explanation
Correct answer: 4
A set with n distinct elements has 2ⁿ total subsets because each element has two independent choices: it may be included or excluded. For A = {a, b}, n = 2, so the number is 2² = 4. Listing them confirms the result: ∅, {a}, {b}, and {a, b}. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A set with n distinct elements has 2ⁿ total subsets because each element has two independent choices: it may be included or excluded. For A = {a, b}, n = 2, so the number is 2² = 4. Listing them confirms the result: ∅, {a}, {b}, and {a, b}. Thus option C is correct.
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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