In a library, Hindi books are \(H=\{h_1,h_2,h_3\}\) and English books are \(E=\{h_3,e_1,e_2\}\). Which set represents the books that belong to at least one category?
Answer and explanation
Correct answer: \(H\cup E=\{h_1,h_2,h_3,e_1,e_2\}\)
The phrase “at least one category” means that a book may be in H, in E, or in both; this is exactly the union. Combining all distinct elements gives \(H\cup E=\{h_1,h_2,h_3,e_1,e_2\}\). The repeated element \(h_3\) is written only once because sets do not contain duplicates. Option B gives only common books, while C and D give books exclusive to one category, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(H\cup E=\{h_1,h_2,h_3,e_1,e_2\}\)
Why is this the correct answer?
The phrase “at least one category” means that a book may be in H, in E, or in both; this is exactly the union. Combining all distinct elements gives \(H\cup E=\{h_1,h_2,h_3,e_1,e_2\}\). The repeated element \(h_3\) is written only once because sets do not contain duplicates. Option B gives only common books, while C and D give books exclusive to one category, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
