From the following Venn diagram identify the number of persons who are either good speakers or post graduates or doctors.
Good Speakers (S) circle includes regions with numbers 3, 2, 4, 1.
Post Graduates (P) circle includes regions with numbers 5, 2, 4, 3.
Doctors (D) circle includes regions with numbers 4, 1, 3, 4.
The question asks for the number of persons who are either good speakers or post graduates or doctors. This corresponds to the union of the three sets (S $\cup$ P $\cup$ D).
The number of elements in the union of sets is the sum of the numbers in all the distinct regions covered by the circles.
These regions are:
– Only Good Speakers (S only): 3
– Only Post Graduates (P only): 5
– Only Doctors (D only): 4
– Good Speakers and Post Graduates only (S $\cap$ P only): 2
– Good Speakers and Doctors only (S $\cap$ D only): 1
– Post Graduates and Doctors only (P $\cap$ D only): 3
– Good Speakers, Post Graduates, and Doctors (S $\cap$ P $\cap$ D): 4
Total number of persons in the union = Sum of numbers in all these regions
Total = 3 + 5 + 4 + 2 + 1 + 3 + 4 = 22.