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Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.
A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. They serve to graphically organise things and highlighting how the items are similar and different.
|UNIT VI – Logical Reasoning (Click below on the topic to read the study notes)
The main aim of the Venn Diagram is to test the validity of arguments through the relation between premises and conclusion by diagrams.
In this example, Whales and Fish belong to two different groups, but there is something common between them. The common feature is, they live in the ocean, and it has easily represented by two circles overlapping to some extent.
There are TEN conditions by which we can test the validity of arguments. The conditions are followings:
Condition 1: If all the items are of different groups, then they will be shown by the diagram as given below.
For e.g. Dog, Cow, Horse
These animals are of three different groups; there is no relation between them. Hence, they will be represented by three different circles.
Condition 2: If the first word is related to the second word, and the second word is related to the third word. Then the representation will be shown by diagram as given below.
E.g., Unit, Tens, Hundreds
Ten units together make one Ten (in one ten, the whole unit is available), and ten tens together make one hundred.
Condition 3: If two different items are entirely related to the third item, they will be shown as below.
E.g., Pen, Pencil, Stationery
Condition 4: If there is some relation between two items, and these two items are completely related to a third item, they will be shown as given below.
E.g., Women, Sisters, Mothers
Some sisters may be mothers and vice-versa. Similarly, some mothers may not be sisters and vice-versa. But all the sisters and mothers belong to women group.
Condition 5: Two items are related to a third item to some extent but not completely, and the first two items totally different.
E.g., Students, Boys, Girls
The boys and girls are different items, while some boys may be students. Similarly, among girls, some may be students.
Condition 6: All the three items are related to one another, but some extent, not completely.
E.g., Boys, Students, Athletes
Some boys may be students and vice-versa. Similarly, some boys may be athletes and vice-versa. Some students may be athletes and vice-versa.
Condition 7: Two items are related to each other completely, and the third item is entirely different from the first two.
E.g., Lions, Carnivorous, Cows
All lions are carnivorous, but no cow is lion or carnivorous.
Condition 8: The first item is completely related to the second, and the third item is partially related to the first and second items.
Eg. Females, Mothers, Doctors
In the example, all Mothers belong to Females, but some Mothers are Doctors, but not all.
Condition 9: First item is partially related to the second, but the third is entirely different from the first two.
E.g., Dogs, Flesh-eaters, Cows
Some dogs are flesh-eaters, but not all while any dog or any flesh-eater cannot be a cow.
Condition 10: The first item is wholly related to the second, and the third item is partially related to the first and second items.
E.g., Males, Fathers, Children