Types of Statements

We will encounter four types of statements (as premises and conclusions).

  • Universal Affirmative - i.e. affirmative declarative sentence with universal quantifier.
  • Universal Negative - i.e. negative declarative sentence with universal quantifier.
  • Particular Affirmative - i.e. affirmative declarative sentence with particular quantifier.
  • Particular Negative - i.e. negative declarative sentence with particular quantifier.

Let’s see them one by one and how they are represented through Venn diagram.

Universal Affirmative

All S are P - We can showcase it using two possible Venn Diagrams. syllogism

All positive propositions beginning with ‘every’, ‘each’ and ‘any’ etc are of this type.
e.g., Every cot is mat. (All cots are mats)
Each student of class V has passed. (All students of class V have passed)
Anyone can do this job. (All can do this job)

Universal Negative

No S is P – We can showcase it using only one possible Venn Diagram syllogism All negative sentences beginning with ‘no one’, ‘none’, ‘not a single’ etc are of this type.
e.g., Not a single student could pass the exam.
None can cross the English channel.

Particular Affirmative

Some S are P – We can showcase it using four possible Venn Diagrams. (It is opposite to No S are P)

The most common way to represent this are: syllogism

But ‘Some S are P’ also includes the possibility that ‘All S are P’ (so we can draw the two diagrams of Universal Affirmative here too). syllogism

Positive propositions beginning with words such as ‘most’, ‘a few’, ‘mostly’, ‘generally’, ‘almost’, ‘frequently’ and ‘often’ etc are of this type.
e.g., Almost all the laptops have been sold (Some laptops have been sold.)
Most of the aspirants will qualify in the examination (Some of the aspirants will qualify in the examination.)

Particular Negative

Some S are not P – We can showcase it using three possible Venn Diagrams.

The most common way to represent this are: syllogism

But ‘Some S are not P’ also includes the possibility that ‘No S is P’ (so we can draw the one diagram of Universal Negative here too). syllogism

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