Two propositions are contradictories if :

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UGC NET Paper 1: Held on 20th Nov 2021 Shift 2
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  1. One is denial or negation of the other 
  2. If they can both be true but cannot both be false 
  3. If they have different subject and predicate term and differ from each other in both quality and quantity 
  4. If they have the same subject and predicate terms but differ from each other only in quantity but not in quality 

Answer (Detailed Solution Below)

Option 1 : One is denial or negation of the other 
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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The square of opposition is a chart that was introduced within classical (categorical) logic to represent the logical relationships holding between certain propositions in virtue of their form.

Key Points

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 The square of opposition:

  • Universals on top vs particulars on the bottom
  • Affirmatives on left vs negatives on right
  • Contradictories (diagonals):

They always have the opposite truth values--you will always be able to determine the truth value of contradictories.

  • Contraries:
    • Two propositions are said to be contraries if they can't both be true, and the truth of one entails the truth of the other. i.e. Two statements are contrary to one another if they are both universals but differ in quality.
    • Contraries cannot at the same time both be true, but can, at the same time, be false.
    • If either of these propositions is true, then the other must be false.
    • Contraries cannot both be true at the same time 
  • Sub-contraries
    • ​The relation between two particular propositions having the same subject and predicate but differing in quality is subcontrary opposition
  • Subalternation
    • It is a relation between the particular statement and the universal statement of the same quality (affirmative or negative) such that the particular is implied by the universal,
  • Opposition:
    • It occurs when two standard-form categorical propositions refer to the same subject and predicate classes but differ in quality, quantity, or both.

Hence we conclude that the correct answer is one is denial or negation of the other 

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