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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 16

If A = {(x, y) : x, y ∈ {1, 2, 3}, x < y} and B = {(x, y) : x + y = 4}, what is A ∩ B?

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Answer and explanation

Correct answer: {(1, 3)}

First list the ordered pairs allowed by x < y: (1,2), (1,3), and (2,3). Now test the second condition x + y = 4. Only (1,3) has sum 4. The pair (3,1) also has sum 4, but it fails x < y, while (2,2) fails the strict inequality. Therefore the intersection contains only {(1,3)}.

Tags

setsordered-pairsintersectionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{(1, 3)}

Why is this the correct answer?

First list the ordered pairs allowed by x < y: (1,2), (1,3), and (2,3). Now test the second condition x + y = 4. Only (1,3) has sum 4. The pair (3,1) also has sum 4, but it fails x < y, while (2,2) fails the strict inequality. Therefore the intersection contains only {(1,3)}.

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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