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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19
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If U has 200 students, 120 take Hindi, 90 take English, and 50 take both languages, how many take neither language?

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Answer and explanation

Correct answer: 40

Let H be the set of students taking Hindi and E the set taking English. By the inclusion–exclusion principle, |H ∪ E| = |H| + |E| − |H ∩ E| = 120 + 90 − 50 = 160. Students taking neither language belong to (H ∪ E)′. Therefore their number is 200 − 160 = 40, so option A is correct.

Related tags

SetsComplementInclusion-ExclusionWord ProblemComplement Of A Set And Its PropertiesMathematicsClass 10 Mcq

Frequently asked questions

What is the correct answer to this question?

40

Why is this the correct answer?

Let H be the set of students taking Hindi and E the set taking English. By the inclusion–exclusion principle, |H ∪ E| = |H| + |E| − |H ∩ E| = 120 + 90 − 50 = 160. Students taking neither language belong to (H ∪ E)′. Therefore their number is 200 − 160 = 40, so 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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10 more MCQs
  1. 1Which element belongs to the power set of A = {1, 2, 3}?
  2. 2If U = {1, 2, 3, 4, 5} and A = {2, 4}, which of the following is a subset of the complement of A?
  3. 3If \(A\subseteq B\), which statement about their complements is true?
  4. 4If U = {1, 2, 3, 4, 5} and A = {2, 4}, what is the complement A'?
  5. 5If U = {a, b, c, d} and B = {a, d}, what is B′, the complement of B?
  6. 6If A ⊆ U, then A′ is a subset of which set?
  7. 7If the universal set U = {1, 2, 3, 4} and A = U, what is A′, the complement of A?
  8. 8If \(U=\{0,1,2,3,4\}\) and \(A=\{0,2,4\}\), how many elements are in \(A'\)?
  9. 9If U = {1, 2, 3, 4, 5, 6} and E = {2, 4, 6}, what is E′?
  10. 10If U = {a, b, c, d} and A = {a, c}, what is A′?
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