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Logical diagrams based situations have their own importance in the context of preparing for any aptitude examination. There are three major types of questions based on diagrams —
(i) Numerical questions on set theory based on venn diagrams
(ii) Logical questions based on set theory
(iii) Questions based on network diagrams.
Let us first take a look at some standard theoretical inputs related to set theory.
Look at the following diagrams:
Figure 1: Refers to the situation where there are two attributes A and B. (Let’s say A refers to people who passed in Physics and B refers to people who passed in Chemistry.) Then the shaded area shows the people who passed both Physics and Chemistry.
In mathematical terms, the situation is represented as:
Total number of people who passed at least 1 subject = A + B – A ∩ B
Figure 2: Refers to the situation where there are three attributes being measured. In the figure below, we are talking about people who passed Physics, Chemistry and/or Mathematics.
In the above figure, the following explain the respective areas:
Area 1: People who passed in Physics only
Area 2: People who passed in Physics and Chemistry only (in other words— people who passed Physics and Chemistry but not Mathematics)
Area 3: People who passed Chemistry only
Area 4: People who passed Chemistry and Mathematics only (also, can be described as people who passed Chemistry and Mathematics but not Physics)
Area 5: People who passed Physics and Mathematics only (also, can be described as people who passed Physics and Mathematics but not Chemistry)
Area 6: People who passed Physics, Chemistry and Mathematics
Area 7: People who passed Mathematics only
Area 8: People who passed in no subjects
Also take note of the following language which there is normally confusion about:
People passing Physics and Chemistry—Represented by the sum of areas 2 and 6
People passing Physics and Maths—Represented by the sum of areas 5 and 6
People passing Chemistry and Maths—Represented by the sum of areas 4 and 6
People passing Physics—Represented by the sum of the areas 1, 2, 5 and 6
In mathematical terms, this means:
Total number of people who passed at least 1 subject =
P + C + M – P ∩ C – P ∩ M – C ∩ M + P ∩ C ∩ M
Let us consider the following question and see how these figures work in terms of real time problem solving:
Q.1. At the birthday party of Sherry, a baby boy, 40 persons chose to kiss him and 25 chose to shake hands with him. 10 persons chose to both kiss him and shake hands with him. How many persons turned out at the party?
(a) 35
(b) 75
(c) 55
(d) 25
From the figure, it is clear that the number of people at the party were 30 + 10 +15 = 55.
We can of course solve this mathematically as below:
Let n(A) = No. of persons who kissed Sherry = 40
n(B) = No. of persons who shake hands with Sherry = 25
and n(A ∩ B) = No. of persons who shook hands with Sherry and kissed him both = 10
Then using the formula, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
n(A ∪ B) = 40 + 25 – 10 = 55
Q.2. In the Mindworkzz club all the members participate either in the Tambola or the Fete. 320 participate in the Fete, 350 participate in the Tambola and 220 participate in both. How many members does the club have?
(a) 410
(b) 550
(c) 440
(d) None of these
The total number of people = 100 + 220 + 130 = 450
Option (d) is correct.
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