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UGC NET Paper 1 - Classical Square of Opposition

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UGC NET Paper 1 ā€¢ Concept 7

Classical Square
of Opposition

Unit 6 ā€¢ Chapter 1

Understanding Logical Relationships

Topic 7: The Four Key Relationships

šŸ“– Based on Ankit Sharma's Book
UGC NET Paper 1 Volume 5 - Logical Reasoning Unlocked

+91 9645160045
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CONCEPT 7

What is the Square of Opposition?

A Classical Tool for Logical Relationships

The Square of Opposition is a fundamental tool in traditional logic that shows how four types of categorical propositions about the same subject and predicate are logically related to each other.

šŸ“ The Four Types of Propositions

A

Universal Affirmative

"All S are P"

Example:
"All birds can fly"

E

Universal Negative

"No S are P"

Example:
"No birds can fly"

I

Particular Affirmative

"Some S are P"

Example:
"Some birds can fly"

O

Particular Negative

"Some S are not P"

Example:
"Some birds cannot fly"

šŸ” Key Classifications

By Quantity:

Universal: A & E (All/No)
Particular: I & O (Some)

By Quality:

Affirmative: A & I (are)
Negative: E & O (are not)

šŸŽÆ What's Next: We'll explore the four key relationships between these propositions: Contradictory, Contrary, Subcontrary, and Subaltern. Each relationship has specific rules about truth and falsity!

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The Classical Square of Opposition

Visual Representation of All Relationships

A Universal Affirmative "All S are P" E Universal Negative "No S are P" I Particular Affirmative "Some S are P" O Particular Negative "Some S are not P" CONTRADICTORY CONTRARY SUBCONTRARY SUBALTERN SUBALTERN

šŸ“‹ Relationship Types

Contradictory: Diagonal (Aā†”O, Eā†”I)
Contrary: Top edge (Aā†”E)
Subcontrary: Bottom edge (Iā†”O)
Subaltern: Vertical sides (Aā†’I, Eā†’O)
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1. Contradictory Relationship

Diagonal Opposites: Aā†”O and Eā†”I

šŸ“– Definition

Contradictory propositions are diagonal opposites in the square. They represent the strongest form of opposition.

A E I O A ā†” O E ā†” I

āš” The Iron Rule

āœ“ They CANNOT both be TRUE
āœ“ They CANNOT both be FALSE
āœ“ If one is TRUE ā†’ the other MUST be FALSE
āœ“ If one is FALSE ā†’ the other MUST be TRUE

šŸ“Š Truth Table

If A is... Then O is... If E is... Then I is...
TRUE FALSE TRUE FALSE
FALSE TRUE FALSE TRUE

šŸ“ Example

A: "All humans are mortal" ā†’ TRUE
O: "Some humans are not mortal" ā†’ FALSE

E: "No birds are apes" ā†’ TRUE
I: "Some birds are apes" ā†’ FALSE

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Contradictory: Exam Questions

Actual UGC NET Examples

Asked in Exam

"All human beings are mortal" and "Some human beings are not mortal" statements are so related that if one of them is true the other must be false and vice versa.

Analysis: A and O propositions - Perfect contradictory relationship

Asked in Exam

"No birds are apes" and "Some birds are apes" are contradictories.

Analysis: E and I propositions - Diagonal opposites

Asked in Exam

"Some cats are not carnivores" (O) is the contradictory of "All cats are carnivores" (A).

Analysis: Clear identification of A-O contradictory pair

Asked in Exam

A proposition and O proposition are contradictories.

Analysis: Direct statement about the A-O contradictory relationship

šŸ’” Exam Strategy

  • Look for statements with opposite quantity AND quality
  • A ā†” O: "All" vs "Some...not"
  • E ā†” I: "No" vs "Some...are"
  • Key phrase: "if one is true, the other MUST be false"
  • Remember: Strongest opposition - no middle ground!
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2. Contrary Relationship

Top Edge: Aā†”E (Both Universal)

šŸ“– Definition

Contrary propositions are both universal but have opposite quality. They occupy the top edge of the square.

A All S are P E No S are P CONTRARY I O

āš” The Contrary Rule

āœ“ They CANNOT both be TRUE
āœ“ They CAN both be FALSE
āœ“ If one is TRUE ā†’ the other MUST be FALSE
āœ“ If one is FALSE ā†’ the other is UNDETERMINED

šŸ“Š Truth Table

If A is... Then E is... Can Both Be?
TRUE FALSE No (Both TRUE)
FALSE UNDETERMINED Yes (Both FALSE)
UNDETERMINED FALSE Yes (Both FALSE)

šŸ“ Example

Case 1: Can both be TRUE?
A: "All monkeys are apes" ā†’ TRUE
E: "No monkeys are apes" ā†’ FALSE (Forced)
ā†’ Cannot both be TRUE āŒ

Case 2: Can both be FALSE?
A: "All birds can fly" ā†’ FALSE (penguins exist)
E: "No birds can fly" ā†’ FALSE (eagles exist)
ā†’ Both FALSE is possible āœ…

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Contrary: Exam Questions

Actual UGC NET Examples

Asked in Exam

To determine which statements are so related that if one of them is true, the other must be false, even though both of them can be false, we need to identify the Contrary relationship.

Analysis: This is the defining characteristic of contrary propositions

Asked in Exam

"No professors are materialists" and "All professors are materialists" are contrary propositions.

Analysis: E and A propositions - both universal, opposite quality

Asked in Exam

"All Monkeys are apes" and "No monkeys are apes" cannot both be true but can both be false.

Analysis: Perfect example of contrary relationship characteristics

Asked in Exam

"No cows are herbivores" is contrary to the proposition "All cows are herbivores".

Analysis: E and A propositions showing contrary relationship

šŸ§  Memory Aid: "CONTRARY"

Cannot both be true
Opposite qualities (affirmative vs negative)
Not necessarily opposite when false
Top edge of the square
Relates universals (A and E)
Allows both to be false
RY - Remember: "If true ā†’ other false, but both can be false"

šŸ’” Exam Strategy

  • Look for two universal statements (All/No)
  • Key phrase: "cannot both be true BUT can both be false"
  • Think of extreme opposites that could both be wrong
  • Example: "All X are Y" and "No X are Y" - both could be false if only some X are Y
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3. Subcontrary Relationship

Bottom Edge: Iā†”O (Both Particular)

šŸ“– Definition

Subcontrary propositions are both particular but have opposite quality. They occupy the bottom edge of the square. This is the mirror opposite of contrary!

A E I Some S are P O Some S are not P SUBCONTRARY

āš” The Subcontrary Rule

āœ“ They CAN both be TRUE
āœ“ They CANNOT both be FALSE
āœ“ If one is FALSE ā†’ the other MUST be TRUE
āœ“ If one is TRUE ā†’ the other is UNDETERMINED

šŸ”„ Mirror Opposite of Contrary

Contrary (Aā†”E)

āŒ Cannot both be TRUE
āœ… Can both be FALSE

Subcontrary (Iā†”O)

āœ… Can both be TRUE
āŒ Cannot both be FALSE

šŸ“Š Truth Table

If I is... Then O is... Can Both Be?
TRUE UNDETERMINED Yes (Both TRUE)
FALSE TRUE No (Both FALSE)
UNDETERMINED TRUE Yes (Both TRUE)

šŸ“ Example

Case 1: Can both be TRUE?
I: "Some cars are e-vehicles" ā†’ TRUE (Teslas exist)
O: "Some cars are not e-vehicles" ā†’ TRUE (gas cars exist)
ā†’ Both TRUE is possible āœ…

Case 2: Can both be FALSE?
Cannot happen! At least one "Some" statement must be true.
ā†’ Both FALSE is impossible āŒ

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Subcontrary: Exam Questions

Actual UGC NET Examples

Asked in Exam

To determine which of the statements are so related that they cannot both be false, although they may both be true, we need to focus on the Subcontrary.

Analysis: This is the defining characteristic of subcontrary propositions

Asked in Exam

"Some cars are e-vehicles" and "Some cars are not e-vehicles" are subcontrary propositions.

Analysis: I and O propositions - both particular, opposite quality

Asked in Exam

"Some saints are materialists" and "Some saints are not materialists" are so related that they cannot both be false, though they can both be true.

Analysis: Perfect subcontrary relationship - at least one must be true

Asked in Exam

I proposition and O proposition are subcontraries.

Analysis: Direct statement about the I-O subcontrary relationship

šŸ¤” Why Can't Both Be False?

Think about it logically:

I: "Some S are P" ā†’ FALSE means NO S are P
O: "Some S are not P" ā†’ FALSE means ALL S are P

But if NO S are P AND ALL S are P are both true...
That's a CONTRADICTION! āš ļø

Therefore, at least ONE of the particular statements (I or O) MUST be true!

šŸ’” Exam Strategy

  • Look for two particular statements (Some...are / Some...not)
  • Key phrase: "cannot both be false BUT may both be true"
  • Remember: This is the mirror opposite of contrary!
  • At least one "Some" statement must always be true
  • Both can be true if the category has diversity
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4. Subaltern Relationship

Vertical Sides: Aā†’I and Eā†’O

šŸ“– Definition

Subaltern propositions have the same quality but different quantity. They occupy the vertical sides of the square. The universal statement is the superaltern, and the particular is the subaltern.

Truth ā†“ Falsity ā†‘ Truth ā†“ Falsity ā†‘ A Superaltern "All S are P" I Subaltern "Some S are P" E Superaltern "No S are P" O Subaltern "Some S are not P" SUBALTERN SUBALTERN

āš” The Subaltern Rule

šŸ”½ Truth flows DOWN:
If Universal (A/E) is TRUE ā†’ Particular (I/O) is TRUE

šŸ”¼ Falsity flows UP:
If Particular (I/O) is FALSE ā†’ Universal (A/E) is FALSE

A ā†’ I Relationship

If A is TRUE:
"All plants are green"
ā†’ I MUST be TRUE
"Some plants are green" āœ…

If I is FALSE:
"Some plants are green" (FALSE)
ā†’ A MUST be FALSE
"All plants are green" āŒ

E ā†’ O Relationship

If E is TRUE:
"No fish are mammals"
ā†’ O MUST be TRUE
"Some fish are not mammals" āœ…

If O is FALSE:
"Some fish are not mammals" (FALSE)
ā†’ E MUST be FALSE
"No fish are mammals" āŒ

āš ļø Important: The flow does NOT work in reverse!
ā€¢ If A is FALSE, I could be TRUE or FALSE (undetermined)
ā€¢ If I is TRUE, A could be TRUE or FALSE (undetermined)

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Subaltern: Exam Question

Actual UGC NET Example

Asked in Exam

"All plants are green organisms" and "Some plants are green organisms" are subalternate as per traditional square of opposition.

Analysis: A and I propositions - same quality (affirmative), different quantity

šŸ“Š Complete Subaltern Truth Table

A ā†’ I Subaltern
A (Universal) I (Particular)
TRUE TRUE āœ“
FALSE Undetermined
Undetermined TRUE
FALSE āœ“ FALSE
E ā†’ O Subaltern
E (Universal) O (Particular)
TRUE TRUE āœ“
FALSE Undetermined
Undetermined TRUE
FALSE āœ“ FALSE

šŸ§  Memory Aid: "Water Flows Down, Fire Rises Up"

šŸ’§ Truth is like water - it flows DOWN from universal to particular
If "All" is true ā†’ "Some" must be true

šŸ”„ Falsity is like fire - it rises UP from particular to universal
If "Some" is false ā†’ "All" must be false

šŸ’” Exam Strategy

  • Look for statements with same quality, different quantity
  • Universal ā†’ Particular: same meaning but weaker claim
  • Remember the flow: Truth ā†“ Falsity ā†‘
  • Aā†’I: Both affirmative (Same subject, same predicate)
  • Eā†’O: Both negative (Same subject, same predicate)
  • The reverse flow does NOT work!
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Complete Summary

All Four Relationships at a Glance

Relationship Propositions Both True? Both False? Key Rule
CONTRADICTORY
Diagonal opposites		 A ā†” O
E ā†” I		 NO NO Opposite truth values always
CONTRARY
Top edge		 A ā†” E NO YES If one true ā†’ other false
SUBCONTRARY
Bottom edge		 I ā†” O YES NO If one false ā†’ other true
SUBALTERN
Vertical sides		 A ā†’ I
E ā†’ O		 MAYBE MAYBE Truth ā†“ Falsity ā†‘

šŸŽÆ Quick Decision Tree

ā“ Are they diagonal opposites? (A-O or E-I)

āœ… YES ā†’ CONTRADICTORY (strongest opposition)

ā“ Are both universal? (A-E)

āœ… YES ā†’ CONTRARY (cannot both be true)

ā“ Are both particular? (I-O)

āœ… YES ā†’ SUBCONTRARY (cannot both be false)

ā“ Same quality, different quantity? (A-I or E-O)

āœ… YES ā†’ SUBALTERN (truth flows down, falsity flows up)

šŸŽÆ Critical Exam Tips

  • Contradictory: "if one true, other MUST be false" - look for A-O or E-I
  • Contrary: "cannot both be true BUT can both be false" - look for A-E
  • Subcontrary: "cannot both be false BUT can both be true" - look for I-O
  • Subaltern: "truth flows down" - look for A-I or E-O vertical pairs
  • Always identify proposition types FIRST (A, E, I, O)
  • Then check their position in the square
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You're Ready!

You now understand all four relationships in the
Classical Square of Opposition

Contradictory

Opposite always

Contrary

Can't both be true

Subcontrary

Can't both be false

Subaltern

Truth ā†“ Falsity ā†‘

šŸ’Ŗ Practice Makes Perfect

The key to mastering the Square of Opposition is practice. Try to identify relationships in sample problems and always draw the square if you're unsure!

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Based on Ankit Sharma's Book - UGC NET Paper 1 Volume 5
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