If U = {x : x ∈ N, 1 ≤ x ≤ 20} and A = {x : x ∈ U, x is a factor of 20}, how many elements does the complement Aᶜ relative to U contain?
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Answer and explanation
Correct answer: 14
The universal set U contains the natural numbers 1 through 20, so |U| = 20. The positive factors of 20 are A = {1,2,4,5,10,20}, giving |A| = 6. Every element of U is either in A or in its complement, so |Aᶜ| = |U| − |A| = 20 − 6 = 14. Therefore option C is correct; six is the size of A, not Aᶜ.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The universal set U contains the natural numbers 1 through 20, so |U| = 20. The positive factors of 20 are A = {1,2,4,5,10,20}, giving |A| = 6. Every element of U is either in A or in its complement, so |Aᶜ| = |U| − |A| = 20 − 6 = 14. Therefore option C is correct; six is the size of A, not Aᶜ.
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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