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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If U = {1, 2, ..., 20}, A = {x : x ∈ U and x ≤ 8}, and B = {x : x ∈ U and x ≥ 14}, what is (A ∪ B)′?

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Answer and explanation

Correct answer: {9, 10, 11, 12, 13}

Within U, set A contains 1 through 8, while set B contains 14 through 20. Their union therefore contains the two outer ranges: {1, ..., 8, 14, ..., 20}. The elements of U that are missing from this union are exactly 9, 10, 11, 12, and 13. Hence (A ∪ B)′ = {9, 10, 11, 12, 13}.

Tags

setsunioncomplementfinite-setsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{9, 10, 11, 12, 13}

Why is this the correct answer?

Within U, set A contains 1 through 8, while set B contains 14 through 20. Their union therefore contains the two outer ranges: {1, ..., 8, 14, ..., 20}. The elements of U that are missing from this union are exactly 9, 10, 11, 12, and 13. Hence (A ∪ B)′ = {9, 10, 11, 12, 13}.

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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