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:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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:
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
