# Ch.7 :- Logic Based Venn Diagrams :- Introduction & Formula

Situation I
When one group of items is completely included in the second Group items and the second, again completely belongs to the third group, then the Venn Diagrams would be as follows:

Ex. : Guitarists, instrumentalists, musicians.Clearly, all guitarists are instrumentalists and in turn all instrumentalists are musicians.

Situation II
If two separate groups of items are completely unrelated to each other, but they are all completely included in the third group, then the relationships can be diagrammatically shown as :

EX. : Carrot, Pumpkin, Vegetable.Carrots and pumpkins are completely unrelated to each other, but they are all Vegetables.

Situation III
When two groups of items have some common relationship and both of them are all inclusive in the  third group, the relationships are shown by two smaller intersecting circles  in a third large circle.

Ex. : Mothers, Sisters, Females.Some mothers may be sisters. So mothers and sisters are represented by two smaller intersecting circles. But,both mother and sisters are females

Situation IV
When one group of items is completely included in the second group, while the third is not related at all with any of these two, the diagrammatic representation is as follows:

Ex. : Indian, Asian, European.Here all the Indians are Asians but European is completely a separate class.

Situation V
If the three groups of items are related to each other in same way,their  mutual relationship is shown as follows:

EX. :  Illiterate people, Unemployed, Poor People.Clearly, some illiterate people are unemployed and some are poor. Also some unemployed are poor people while some are illiterate, poor and unemployed, all the three .

Situation VI
When two groups of items are completely unrelated to each other, while they are partly related with the third.group of items, their mutual relationship is shown as below:

EX. : Clothes, flowers, bright things.Some clothes are bright and some flowers are also bright, but not all bright things are clothes or flowers.

Situation VII
If one group of items is completely included in the second group of items and the third group of items is partly related with the first two groups,their relationship is shown as below:

EX. : Females, nieces, cousins.All nieces are females while only some cousins can be nieces and females both or only females.

Situation VIII
If one group of items is partly included in the second 3 group of items and the third group is completely unrelated to these two groups, their relationship is diagrammatically shown as :

EX. :  Students, scholars, book.Some students are scholars while book is unrelated to both of these groups.

Situation IX
When the groups of items belong to completely different three distinct groups, their relationship is shown by three disjoint circles as :

Ex. : Sun, Pluto, Earth .These belong to three different classes. Sun is a star,Pluto is a divert planet while Earth is Planet.

✦ Directions for Q. No. 1 to 4 : Each of the questions given below contains three group of items.You are to choose from the following five. numbered diagrams, a diagram that depicts the correct relationship among the three groups of items in each of the question

1. Moon, Earth, Universe –
2. India, Pakistan, Asia
3. Batsman, Cricketer, Stick-
4. Book,Pen, Pencil.

Sol. :
1 (a) Moon and Earth are not related with one another. Moon is a satellite, while Earth is planet. But both of them are included in the universe. So, the correct option is (a)
2 (b) India and Pakistan are two different countries, but they are both the parts of Asia.
3 (c) All batsmen are cricketers, but stick is distinct and exclusive group of these two.
4 (d) Book, Pencil and Pen are items related to learning, but they are quite three distinct groups.

EX. : Which of the following diagram correctly represents the relationship among Tennis fans, Cricket players and Students?

Sol. Bidi smokers are Smokers and a Cancer patient may be either a Smoker or a Bidi smoker or a Non-smoker.Therefore, the third object shares a common relationship with the first and second objects. Hence,diagram (b) is the correct answer.