Venn Diagrams Method

Syllogism (Notes New)

Venn Diagrams Method

Step I : Draw standard representations for the statements separately.

Note : By standard representation we mean a representation which is the most common and usually sufficient way to denote the statement.

For example : “some X any “y” can be represented as :-

But, for all practical purposes the first of these representation suffices.

Given below is a table of standard representation.

          

Step II: Now try to combine the representation (as shown in step I) in as many ways as possible.

Note : When we say as many ways as possible, we mean that you should combine the representation in all possible ways. For example, if statement (1) is “All X are “Y” and statement (2) is “same Y are Z” then the standard representation are:-

                  

They can be combined in more than one ways and the possible ways are:-

                   

Therefore step II tells you to draw all possible combinations.

Step III. Finally, make interpretations from the combined figures (obtained from step II). Any given conclusion will be true if and only if it is supported by all the combined figures and no combined figures contradicts it.

For example : In the illustration in step II, we see that a conclusion that “some X are Z” is supported by fig.(ii) and (iii) but not by fig (i). since it is not supported by all the figures, it does not follow.

Example :1

Statements : A. All cats are bats.

                   B. All bats are tables.

Conclusions: I . Some tables are bats.

                   II. Some tables are cats.

Solution :

Step I : we draw standard representation.

          

C= cats, B= bats, T= tables

Step II : Figure (A) and figure (B) can be combined in only one way:-

                   

Step III : We see that both conclusions : “some tables are bats” and “some tables are cats” are supported by the combined figure. Hence both the conclusions follow.

Example : 2

Statements : A. No tables are watches.

                   B. Some watches are lamps.

Conclusions : I . Some lamps are not tables.

                   II. Some lamps are tables.

Solution :

Step I : we draw standard representation.

          

T = tables, w= Watches,        L= Lamps

Step II : Now we combine the two figures in all possible ways. They are-

          

Step III: We see that the conclusion “Some lamps are not tables” is always supported by all the possible combinations. Hence, conclusion (I) “some lamps are not tables” is true.