# 5) Construct two squares of opposition, one traditional, the other m

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5) Construct two squares of opposition, one traditional, the
other modern, using the terms professors and great
teachers.
Solution
Squares of Opposition :
A square of opposition shows the logical relations among
categorical statements. There are two squares of
opposition:
1.The Modern Square of Opposition :
The only logical relation in the Modern Square of
To say that two statements are contradictory to each other
means that they necessarily have opposite truth value.
That is, if one of them is true, the other must be false, and
if one of them is false, the other must be true.
There are mainly 4 types of statements.Let us say S and P
are 2 sets. By using these 2 sets the types of statements
can be written as:
A : All S are P

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E : No S are P
I : Some S are P
O : Some S are not P
For example, the A statement All bats are mammals and
the O statement Some bats are not mammals contradict
each other.
The contradictory relation also exists between the E
statement No swans are black birds and the I statements
Some swans are black birds.
We can use Venn Diagrams to illustrate why the
contradictory relation holds between the A and O
statements. When the A statement is true, the area is
empty. But if the area is empty, then no member of S can
be in the area . This contradicts the O statement, which
says that there is at least one member of S in the area ,
i.e., the area is not empty.
If we assume that the set denoted by the subject term
cannot be an empty set, then there are four logical
relations among the A, E, I, O statements. They are shown
in the Traditional Square of Opposition. The four relations
are:
Contrary
Subcontrary

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5) Construct two squares of opposition, one traditional, the other modern, using the terms professors and great teachers. Solution Squares of Opposition : A square of opposition shows the logical relations among categorical statements. There are two squares of opposition: 1.The Modern Square of Opposition : The only logical relation in the Modern Square of Opposition is the contradictory relation. The Contradictory Relation To say that two statements are contradictory to each other means that they necessarily have opposite truth value. That is, if one of them is true, the other must be false, and if one of them is false, the other must be true. There are mainly 4 types of statements.Let us say S and P are 2 sets. By using these 2 sets the types of statements can be written as: A : All S are P E : No S are P I : Some S are P O : Some S are not P For example, the A statement “All bats are mammals” and the O statement “Some bats are not mammals” contradict each other. The contradictory relation also ex ists between the E statement “No swans are black birds” and the I statements “Some swans are black birds.” We can use Venn Diagrams to illustrate why the contradictory relation holds between the A and O statements. When the A statement is true, the area i s empty. But if the area is empty, then no member of S can be in the area . This contradicts the O statement, which says that there is at least one member of S in the area , i.e., the area is not empty. 2.The ...
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I was having a hard time with this subject, and this was a great help.

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