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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 10
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For sets A, B, and C, consider the identity (A \ B) ∩ C = A ∩ (C \ B). Which statement is correct?

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Answer and explanation

Correct answer: It is always true.

An element belongs to the left side exactly when it is in A but not in B, and also in C. Thus it is simultaneously in A and C and outside B. The right side describes precisely the same condition: it is in A and in C \ B, meaning it belongs to C but not to B. Since both sides contain exactly the same elements, the identity is true for all sets A, B, and C.

Tags

setsset-identitydifferenceintersectiondistributive-lawOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

It is always true.

Why is this the correct answer?

An element belongs to the left side exactly when it is in A but not in B, and also in C. Thus it is simultaneously in A and C and outside B. The right side describes precisely the same condition: it is in A and in C \ B, meaning it belongs to C but not to B. Since both sides contain exactly the same elements, the identity is true for all sets A, B, and C.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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10 more MCQs
  1. 1If A = [1, 4] and B = (2, 5), what is A ∩ B?
  2. 2If A = (0, 3) and B = [3, 7], what is A ∩ B?
  3. 3If A = [−3, 2] and B = [0, 5], what is A ∪ B?
  4. 4If A = (1, 2) and B = (3, 4), how should A ∪ B be written?
  5. 5If A = (−∞, 4] and B = (1, ∞), what is A ∩ B?
  6. 6If A = {x ∈ R : x ≤ 0} and B = {x ∈ R : x ≥ 0}, what is A ∩ B?
  7. 7If A = (−4, 1] and B = [−2, 3), what is A \ B?
  8. 8If A = {x : x is a positive multiple of 2 or 3 less than 12}, what is A?
  9. 9If \(A=\{1,2,3,4\}\) and \(B=\{2,3\}\), which statement about \(A-B\) is correct?
  10. 10If A ⊆ B, which of the following statements is always true?
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