If A = {p, q, r}, how many non-empty proper subsets does A have?
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Answer and explanation
Correct answer: 6
A set with three elements has 2^3 = 8 total subsets in its power set. A proper subset cannot be equal to the original set A, so remove A itself. A non-empty subset cannot be the empty set, so remove ∅ as well. Thus, the number of non-empty proper subsets is 8 − 2 = 6. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A set with three elements has 2^3 = 8 total subsets in its power set. A proper subset cannot be equal to the original set A, so remove A itself. A non-empty subset cannot be the empty set, so remove ∅ as well. Thus, the number of non-empty proper subsets is 8 − 2 = 6. Option C 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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