किसी समूह में 15 व्यक्ति हैं; जिनमें से 7 फ्रेंच पढ़ सकते हैं, 8 अंग्रेजी पढ़ सकते हैं, जबकि 3 इन दोनों भाषाओं में से कोई भी भाषा नहीं पढ़ सकते । कितने व्यक्ति यथार्थतः एक भाषा पढ़ सकते हैं?
सही उत्तर (B) 9 है।
व्याख्या:
Total people = 15. Let F be the set of French readers and E be the set of English readers. Neither = 3. Therefore, the number of people who can read at least one language is 15 - 3 = 12. Using the principle of inclusion-exclusion: n(F union E) = n(F) + n(E) - n(F intersection E), we get 12 = 7 + 8 - n(F intersection E), which gives n(F intersection E) = 3 (people who read both languages). The number of people who can read only French = n(F) - n(F intersection E) = 7 - 3 = 4. The number of people who can read only English = n(E) - n(F intersection E) = 8 - 3 = 5. Therefore, the total number of people who can read exactly one language = (only French) + (only English) = 4 + 5 = 9? Wait, let's recalculate: 4 + 5 = 9? Let's check options: 10, 9, 5, 4. Total reading one language = n(F) + n(E) - 2 * n(both) = 7 + 8 - 2(3) = 15 - 6 = 9. Wait, let's check option index 1 (9).
In English (Question & Model Answer)
In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. Find the number of people who can read exactly one language.
The correct answer is (B) 9.
Explanation:
Total people = 15. Let F be the set of French readers and E be the set of English readers. Neither = 3. Therefore, the number of people who can read at least one language is 15 - 3 = 12. Using the principle of inclusion-exclusion: n(F union E) = n(F) + n(E) - n(F intersection E), we get 12 = 7 + 8 - n(F intersection E), which gives n(F intersection E) = 3 (people who read both languages). The number of people who can read only French = n(F) - n(F intersection E) = 7 - 3 = 4. The number of people who can read only English = n(E) - n(F intersection E) = 8 - 3 = 5. Therefore, the total number of people who can read exactly one language = (only French) + (only English) = 4 + 5 = 9? Wait, let's recalculate: 4 + 5 = 9? Let's check options: 10, 9, 5, 4. Total reading one language = n(F) + n(E) - 2 * n(both) = 7 + 8 - 2(3) = 15 - 6 = 9. Wait, let's check option index 1 (9).