GATE 1998
March 18, 2025GATE 1998
March 18, 2025GATE 1998
| Question 39 |
In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada. 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada whereas 13 persons speak both Kannada and English. How many people speak all three languages?
| 9 | |
| 8 | |
| 7 | |
| 6 |
Question 39 Explanation:
Let A be the people who speaks English.
Let B be the people who speaks Hindi.
Let C be the people who speaks Kannada.
(A∪B∪C) = A + B + C – (A∩B) – (B∩C) – (C∩A) + (A∩B∩C)
28 = 18 + 15 + 22 – 9 – 11 – 13 + (A∩B∩C)
∴ (A∩B∩C) = 6
Let B be the people who speaks Hindi.
Let C be the people who speaks Kannada.
(A∪B∪C) = A + B + C – (A∩B) – (B∩C) – (C∩A) + (A∩B∩C)
28 = 18 + 15 + 22 – 9 – 11 – 13 + (A∩B∩C)
∴ (A∩B∩C) = 6
Correct Answer: D
Question 39 Explanation:
Let A be the people who speaks English.
Let B be the people who speaks Hindi.
Let C be the people who speaks Kannada.
(A∪B∪C) = A + B + C – (A∩B) – (B∩C) – (C∩A) + (A∩B∩C)
28 = 18 + 15 + 22 – 9 – 11 – 13 + (A∩B∩C)
∴ (A∩B∩C) = 6
Let B be the people who speaks Hindi.
Let C be the people who speaks Kannada.
(A∪B∪C) = A + B + C – (A∩B) – (B∩C) – (C∩A) + (A∩B∩C)
28 = 18 + 15 + 22 – 9 – 11 – 13 + (A∩B∩C)
∴ (A∩B∩C) = 6