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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 18

If A ∩ (B ∪ C) = A, which conclusion must be true?

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Answer and explanation

Correct answer: A ⊆ B ∪ C

For any sets X and Y, the equality X ∩ Y = X holds exactly when every element of X is also an element of Y; in other words, X ⊆ Y. Here X is A and Y is B ∪ C. Thus every element of A must belong to B or C, so A ⊆ B ∪ C. No reverse inclusion is required.

Tags

setsintersectionsubsetunionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A ⊆ B ∪ C

Why is this the correct answer?

For any sets X and Y, the equality X ∩ Y = X holds exactly when every element of X is also an element of Y; in other words, X ⊆ Y. Here X is A and Y is B ∪ C. Thus every element of A must belong to B or C, so A ⊆ B ∪ C. No reverse inclusion is required.

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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