If U = {1,2,…,18} and A′ = {2,3,5,7,11,13,17}, how many elements are in A?
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Answer and explanation
Correct answer: 11
The universal set U has 18 elements. The given complement A′ contains 7 elements. Since A and A′ partition U into disjoint parts, |A| + |A′| = |U|. Therefore, |A| = 18 − 7 = 11. The actual elements of A are the members of U that are not listed in A′, but only the cardinality is required.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The universal set U has 18 elements. The given complement A′ contains 7 elements. Since A and A′ partition U into disjoint parts, |A| + |A′| = |U|. Therefore, |A| = 18 − 7 = 11. The actual elements of A are the members of U that are not listed in A′, but only the cardinality is required.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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