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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 10

If A \ (B ∪ C) is to be written using only intersection and set difference, which form is correct?

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Answer and explanation

Correct answer: (A \ B) ∩ (A \ C)

An element belongs to A \ (B ∪ C) when it is in A but not in B ∪ C. Not being in B ∪ C means that it is neither in B nor in C. Thus the element must belong simultaneously to A \ B and A \ C. Consequently, A \ (B ∪ C) = (A \ B) ∩ (A \ C). This is the set-difference form of De Morgan’s law.

Tags

setsset-differenceDe-Morgan-lawintersectionunionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

(A \ B) ∩ (A \ C)

Why is this the correct answer?

An element belongs to A \ (B ∪ C) when it is in A but not in B ∪ C. Not being in B ∪ C means that it is neither in B nor in C. Thus the element must belong simultaneously to A \ B and A \ C. Consequently, A \ (B ∪ C) = (A \ B) ∩ (A \ C). This is the set-difference form of De Morgan’s law.

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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