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

If A △ B = (A \ B) ∪ (B \ A), |A △ B| = 34, and |A ∪ B| = 51, what is |A ∩ B|?

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Answer and explanation

Correct answer: 17

The symmetric difference A △ B consists of the elements belonging to exactly one of the two sets. The union contains those elements together with the common elements in A ∩ B. Therefore |A ∪ B| = |A △ B| + |A ∩ B|. Substituting the values gives 51 = 34 + |A ∩ B|, so |A ∩ B| = 17.

Tags

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

Frequently asked questions

What is the correct answer to this question?

17

Why is this the correct answer?

The symmetric difference A △ B consists of the elements belonging to exactly one of the two sets. The union contains those elements together with the common elements in A ∩ B. Therefore |A ∪ B| = |A △ B| + |A ∩ B|. Substituting the values gives 51 = 34 + |A ∩ B|, so |A ∩ B| = 17.

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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