Syllogism

A syllogism or logical appeal is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form.In such questions two or more statements are given and these statements are followed by two or more conclusions. The candidate is required to find out which of the conclusions logically follow from the given statements.

For such questions, the candidates should take the help of Venn diagrams. On the basis of the given statements, the candidate should draw all the possible diagrams, and then he should drive the solution from each of these diagrams separately. Finally, the answer common to all the diagrams is taken.

Example:     

Statements:

  1. All cats are dogs.
  2. All dogs are bulls.

Conclusions:

  1. Some cats are not bulls.
  2. Some bulls are cats.
  3. All bulls are cats.
  4. All cats are bulls.

Answer:       On the basis of both statements, the following one diagram is possible.

From the diagram it is clear that II and IV conclusions logically follow.

Example:      

Statements:

  1. Some dogs are asses.
  2. Some asses are bulls.

Conclusions:

  1. Some asses are not dogs.
  2. Some dogs are bulls.

 

 Answer:       From these statements the following diagrams are possible____

From these diagrams neither I nor II follow.

The Euler’s circles or Venn diagrams

          Venn diagrams or set diagrams are diagrams that show all hypothetically possible logical relations between finite collections of sets (groups of things). There is a pictorial way of representing the propositions, formulated by Euler, an ancient mathematician. Suppose that the proposition is trying to relate the subject (S) with the predicate (P). Then there are four ways in which the relation could be made according to the four propositions:

The following three figures represents, Some B are not A.

Syllogism is a case of mediate inference because in syllogism we draw conclusions from two or more given statements.