Analysis based Venn diagrams
In these types of questions, generally a Venn diagram comprising of different geometrical figures is given. Each geometrical figure in the diagram represents a certain class. The candidate is required to study and analyze the figure carefully and then answer the given questions based on it.
To solve such questions, a student should have solid grasp on these six conceptual terms:
- AND – It’s intersection (A Ո B)
- OR – It’s union (A U B)
- At least
- At most
Let’s understand them using a couple of examples.
Let us consider a scenario where we have people speaking one or more of the given three languages - English, Sanskrit and German.
Number of people who speak:
only English = 35
English = 35 + 13 + 9 + 12
German AND English = 12 + 9
German AND English only = 12
German OR English = 35 + 24 + 12 + 13 + 19 + 9
German OR English only = 35 + 12 + 24
German only OR English only = 24 + 35
not German OR English = (German OR English)’ = 27
at least 2 languages = 12 + 13 + 19 + 9 (i.e. those who speak 2 or 3 languages)
at most 2 languages = 35 + 24 + 27 + 12 + 19 + 13 or Total – 9 (i.e. those who speak 2 or 1 languages)
Q. The following figure shows the viewership of two leading news channels, as found in a sample survey. Find out the number of people who do not watch any news channel.
(a) 175 (b) 75 (c) 195 (d) 135
People who watch Republic OR ZEE News (i.e. atleast one channel) = 85 + 200 - 60 = 225
(we subtracted 60 as otherwise it would have been counted twice)
So, people who do not watch any news channel = (Republic OR ZEE News)' = Total number of people - 225 = 420 - 225 = 195
People who watch only Republic = 85 - 60 = 25
People who watch only ZEE News = 200 - 60 = 140
So, people who watch Republic OR ZEE News (i.e. atleast one channel) = 25 + 140 + 60 = 225
And people who do not watch any news channel = (Republic OR ZEE News)'= Total number of people - 225 = 420 - 225 = 195