Equivalent Propositions in Logic
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Questions and Answers

What is the main objective of equivalent propositions in the formulation of an argument?

  • To clarify the meaning of the original proposition (correct)
  • To change the quantity of the subject term
  • To illustrate the difference between main forms of eduction
  • To introduce new information

    • What is the process of eduction that involves changing the quality of the proposition and changing the predicate term to its contradictory or complement?

  • Ob-version (correct)
  • Restating propositions
  • Contra-position
  • Conversion

    • What is the role of the subject term in the process of ob-version?

  • To illustrate the difference between main forms of eduction
  • To introduce new information
  • To retain the quantity of the proposition (correct)
  • To change the quantity of the proposition

    • What is the result of changing the obvertend to its obverse?

    <p>A new proposition with the same meaning</p> Signup and view all the answers

    What is the term used to describe the original proposition in the process of ob-version?

    <p>Obvertend</p> Signup and view all the answers

    What is the purpose of the three rules in the process of ob-version?

    <p>To ensure the correct formation of the obverse</p> Signup and view all the answers

    What is the main requirement of Rule 1 in conversion?

    <p>Change the subject and predicate of the convertend</p> Signup and view all the answers

    What is the first step in applying the rules of obversion?

    <p>Retain the subject term and its quantity</p> Signup and view all the answers

    What happens to the quality of the proposition in conversion according to Rule 2?

    <p>It is always retained</p> Signup and view all the answers

    What is the result of obverting the proposition 'All senators are elected officials'?

    <p>No senators are non-elected officials</p> Signup and view all the answers

    What is the implication of 'do not extend' in Rule 3?

    <p>Do not change the terms of the convertend</p> Signup and view all the answers

    What is the type of conversion that allows a decrease in the quality of terms?

    <p>Partial conversion</p> Signup and view all the answers

    Which of the following is a valid application of obversion?

    <p>A to E</p> Signup and view all the answers

    What is the logical relationship between the obvertend and its obverse?

    <p>They are always logically equivalent</p> Signup and view all the answers

    What is the result of violating Rule 3 in conversion?

    <p>A particular term becomes universal</p> Signup and view all the answers

    What is the convertend in the example given?

    <p>Some women are politicians</p> Signup and view all the answers

    What is the purpose of the third rule of obversion?

    <p>To substitute the predicate with a contradictory term</p> Signup and view all the answers

    What is the result of obverting the proposition 'All Filipinos are Asians'?

    <p>No Filipinos are non-Asians</p> Signup and view all the answers

    What is the difference between the convertend and converse of a proposition?

    <p>The convertend has a particular subject term and the converse has a universal predicate term</p> Signup and view all the answers

    What is the process of combining conversion and obversion called?

    <p>Contraposition</p> Signup and view all the answers

    What happens to the quality and quantity of the proposition during contraposition?

    <p>They are left unaltered</p> Signup and view all the answers

    What is the result of applying Rule 1 of contraposition?

    <p>The subject term and predicate term are swapped</p> Signup and view all the answers

    What is the purpose of Rule 2 of contraposition?

    <p>To substitute the new subject and predicate terms with their contradictory or complementary terms</p> Signup and view all the answers

    What is the relationship between the contraponend and the contrapositive?

    <p>The contraponend is the original proposition and the contrapositive is the new proposition</p> Signup and view all the answers

    What type of propositions is simple contraposition applicable for?

    <p>A to A and O to O propositions</p> Signup and view all the answers

    What is the correct succession order for contraposition?

    <p>Contraponend, Obverse, Converse, Obverse</p> Signup and view all the answers

    What type of proposition is 'All men are mortal beings' an example of?

    <p>A proposition</p> Signup and view all the answers

    What is the contrapositive of the proposition 'All men are mortal beings'?

    <p>All immortal beings are non-men</p> Signup and view all the answers

    What is the result of applying contraposition to 'Some birds are not flying animals'?

    <p>Some non-flying animals are not birds</p> Signup and view all the answers

    What does the mnemonic 'ContrApositiOn' represent?

    <p>Legitimate in general for A and O propositions</p> Signup and view all the answers

    Study Notes

    Equivalent Propositions

    • An equivalent proposition is a proposition with the same meaning or truth-value as the original proposition.
    • It is the second type of immediate inference, also known as eduction or restating propositions.

    The Three Equivalent Propositions (Eduction)

    • Obversion
    • Conversion
    • Contraposition

    Obversion

    • A process of eduction consisting of two changes:
      • Changing the quality of the proposition (leaving the quantity the same)
      • Changing the predicate term to its contradictory or complement
    • Three rules to observe:
      1. Retain the subject and the quantity of the proposition
      2. Change the quality of the proposition
      3. Substitute the predicate with a contradictory term
    • Applicable to all four categorical propositions (A, E, I, O)

    Conversion

    • A process of eduction involving two changes:
      • Switching the subject term and the predicate term (leaving the quality and quantity of the proposition unaltered)
    • Three rules to observe:
      1. Retain the subject and the quantity of the proposition
      2. Retain the quality of the proposition
      3. Do not extend any term
    • Two types of conversion:
      • Absolute or simple conversion
      • Partial conversion

    Contraposition

    • A process of eduction combining conversion and obversion
    • Consists of two changes:
      • Switching the subject term and the predicate term (leaving the quality and quantity of the proposition unaltered)
      • Complementing both the new subject and predicate terms
    • Three rules to observe:
      1. Interchange the subject and the predicate terms
      2. Substitute the new subject and predicate terms with their contradictory or complementary term
    • Applicable only to "A to A" and "O to O" propositions under simple contraposition, and "E to O" propositions under partial contraposition. Not applicable to "I to I" propositions.

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    Learn about equivalent propositions, a fundamental concept in logical reasoning. Understand the importance of equivalent propositions in forming arguments and identify differences between main forms of education. Test your knowledge with this quiz!

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