Write your answers in the form of a complete English sentence. Which of the statements are equivalent to the given statement? a) Given Statement: Whoever writes the exam has a proper ID card. • Conversion: • Contraposition: • Obversion: • Negation: b) Given Statement: There are forced labor camps in China. • Conversion: • Contraposition: • Obversion:
Write your answers in the form of a complete English sentence. Which of the statements are equivalent to the given statement? a) Given Statement: Whoever writes the exam has a proper ID card. • Conversion: • Contraposition: • Obversion: • Negation: b) Given Statement: There are forced labor camps in China. • Conversion: • Contraposition: • Obversion:
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Directions: Determine the conversion, contraposition, obversion, and negation of the given statements.
Write your answers in the form of a complete English sentence. Which of the statements are equivalent to the given statement?
a) Given Statement: Whoever writes the exam has a proper ID card.
• Conversion:
• Contraposition:
• Obversion:
• Negation:
b) Given Statement: There are forced labor camps in China.
• Conversion:
• Contraposition:
• Obversion:
• Negation:
![Statement Equivalences
The quality of a statement refers to the notion of a statement being affirmative or negative. The
quantifier refers to either the universal or existential/particular quantifier.
TYPE ONE: CONVERSION
Rule: Keeps the quantifier and quality of a statement but switches the terms.
Switching terms maintains equivalence in E and I statements.
Switching terms do not maintain equivalence in A and O statements.
TYPE TWO: CONTRAPOSITION
Rule: Keeps the quantifier and quality of a statement but switches and negates both terms.
Switching and negating both terms maintains equivalence in A and O statements.
Switching and negating both terms don't maintain equivalence in E and I statements.
TYPE THREE: OBVERSION
Rule: Uses same quantifier, but changes the quality of the statement and negates predicate.
Changing quality and negating the predicate term maintains equivalence in all statements.
TYPE FOUR: NEGATION (CONTRADICTORIES)
Rule: Denies A, E, I, O
~A=0 ~E=I
~I = E
~O=A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff97c0725-689e-40d7-87a0-46553d65cfc3%2F84c58888-8010-4137-a0ca-563aab022b8e%2Fjzxti04_processed.png&w=3840&q=75)
Transcribed Image Text:Statement Equivalences
The quality of a statement refers to the notion of a statement being affirmative or negative. The
quantifier refers to either the universal or existential/particular quantifier.
TYPE ONE: CONVERSION
Rule: Keeps the quantifier and quality of a statement but switches the terms.
Switching terms maintains equivalence in E and I statements.
Switching terms do not maintain equivalence in A and O statements.
TYPE TWO: CONTRAPOSITION
Rule: Keeps the quantifier and quality of a statement but switches and negates both terms.
Switching and negating both terms maintains equivalence in A and O statements.
Switching and negating both terms don't maintain equivalence in E and I statements.
TYPE THREE: OBVERSION
Rule: Uses same quantifier, but changes the quality of the statement and negates predicate.
Changing quality and negating the predicate term maintains equivalence in all statements.
TYPE FOUR: NEGATION (CONTRADICTORIES)
Rule: Denies A, E, I, O
~A=0 ~E=I
~I = E
~O=A
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