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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 10
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Which of the following statements is always true for sets?

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Answer and explanation

Correct answer: \(A-(B\cup C)=(A-B)\cap(A-C)\)

An element belongs to \(A-(B\cup C)\) exactly when it is in A and is in neither B nor C. The same condition means that it belongs to both \(A-B\) and \(A-C\). Therefore, \(A-(B\cup C)=(A-B)\cap(A-C)\). This is a difference form of De Morgan’s law, so option C is always true.

Related tags

SetsSet DifferenceDe Morgan LawsUnionIntersectionOperations On Sets (UnionDifference)Operations On Sets Union Intersection DifferenceMathematics

Frequently asked questions

What is the correct answer to this question?

\(A-(B\cup C)=(A-B)\cap(A-C)\)

Why is this the correct answer?

An element belongs to \(A-(B\cup C)\) exactly when it is in A and is in neither B nor C. The same condition means that it belongs to both \(A-B\) and \(A-C\). Therefore, \(A-(B\cup C)=(A-B)\cap(A-C)\). This is a difference form of De Morgan’s law, so option C is always true.

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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  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?
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  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?
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