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UPSC Prelims

Mathematics

Theme:

Sets and Functions / समुच्चय और फलन

Q52 2019, Sets and Functions

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. The number of people who can read exactly one language is

किसी समूह में 15 व्यक्ति हैं; जिनमें से 7 फ्रेंच पढ़ सकते हैं, 8 अंग्रेज़ी पढ़ सकते हैं, जबकि 3 इन दोनों भाषाओं में से कोई भी भाषा नहीं पढ़ सकते। कितने व्यक्ति यथार्थतः एक भाषा पढ़ सकते हैं ?

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• In a group of 15 people 3 cannot read any of two languages.

• So, n(A ∪ B) = 12, n(A) = 7, n(B) = 8. And we have n(A ∪ B) = n(A) + n(B) - n(A ∩ B) By putting the values, we have 12 = 7 + 8 - n(A ∩ B).

• So, n(A ∩ B) = 3.

• So, total number of people who can read exactly one language = (7 - 3) + (8 - 3) = 4 + 5 = 9.

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