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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 10

If U = {1, 2, ..., 10} and A = {x : x ∈ U and x² − 11x + 30 = 0}, what is A' ∩ {5, 6, 7, 8}?

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Answer and explanation

Correct answer: {7, 8}

First factor the quadratic: x² − 11x + 30 = (x − 5)(x − 6). Thus the roots are x = 5 and x = 6, and both belong to U, so A = {5, 6}. The complement A' in U contains every element of U except 5 and 6. Intersecting A' with {5, 6, 7, 8} removes 5 and 6 and leaves {7, 8}. Therefore, option A is correct.

Tags

setscomplementintersectionquadratic equationrootsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{7, 8}

Why is this the correct answer?

First factor the quadratic: x² − 11x + 30 = (x − 5)(x − 6). Thus the roots are x = 5 and x = 6, and both belong to U, so A = {5, 6}. The complement A' in U contains every element of U except 5 and 6. Intersecting A' with {5, 6, 7, 8} removes 5 and 6 and leaves {7, 8}. Therefore, 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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