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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 19

If U has n elements and A has r elements, how many elements are in A′?

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Answer and explanation

Correct answer: n − r

A′ consists of all elements of the universal set U that do not belong to A. Assuming A ⊆ U, the elements of U are divided into two disjoint parts: A and A′. Hence, |U| = |A| + |A′|, so n = r + |A′|. Rearranging gives |A′| = n − r. Thus option B is correct.

Tags

setscomplementcardinality formulauniversal setComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

n − r

Why is this the correct answer?

A′ consists of all elements of the universal set U that do not belong to A. Assuming A ⊆ U, the elements of U are divided into two disjoint parts: A and A′. Hence, |U| = |A| + |A′|, so n = r + |A′|. Rearranging gives |A′| = n − r. Thus option B 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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