If A = {a, b, c, d}, how many subsets of A contain at least one element?
Answer and explanation
Correct answer: 15
A has four distinct elements. Each element can independently be either included or excluded, so the total number of subsets is 2⁴ = 16. Exactly one of these subsets is empty, namely ∅. The phrase “at least one element” excludes that empty subset, so the number of non-empty subsets is 16 − 1 = 15. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A has four distinct elements. Each element can independently be either included or excluded, so the total number of subsets is 2⁴ = 16. Exactly one of these subsets is empty, namely ∅. The phrase “at least one element” excludes that empty subset, so the number of non-empty subsets is 16 − 1 = 15. Hence option A 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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