If U = {x ∈ ℤ : 0 ≤ x ≤ 20} and A = {x ∈ U : x² − 9x + 20 = 0}, how many elements of A' are less than 5?
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Answer and explanation
Correct answer: 4
Factor the equation as x² − 9x + 20 = (x − 4)(x − 5) = 0. Thus, A = {4, 5}. The elements of U that are less than 5 are {0, 1, 2, 3, 4}. Because 4 belongs to A, it is excluded from A'. Therefore, the elements of A' less than 5 are {0, 1, 2, 3}, which has 4 elements. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Factor the equation as x² − 9x + 20 = (x − 4)(x − 5) = 0. Thus, A = {4, 5}. The elements of U that are less than 5 are {0, 1, 2, 3, 4}. Because 4 belongs to A, it is excluded from A'. Therefore, the elements of A' less than 5 are {0, 1, 2, 3}, which has 4 elements. Hence, option A is correct.
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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