Logical Conversion, Obversion, and Contraposition: Exercises in Categorical Proposition Analysis
Overview
This document presents structured exercises on fundamental logical operations applied to categorical propositions. It covers the conversion, obversion, and contraposition of various propositions, along with inference problems based on given logical statements, designed to develop students' understanding of categorical logic and valid logical transformations.
What this coursework covers
- Exercise A: Conversion of categorical propositions and equivalence analysis
- Exercise B: Obversion of propositions and negation patterns
- Exercise C: Contraposition of propositions and logical equivalence determination
- Exercise D: Inference problems based on a true categorical statement about socialists and pacifists
- Exercise E: Inference problems based on a true statement about scientists and philosophers (incomplete)
Preview
Copi, Irving M. Introduction to Logic, 14th Edition. Routledge.
EXERCISE A INSTRUCTIONS
State the converses of the following propositions, and indicate which of them are equivalent to the given propositions:
PROBLEMS
1. No people who are considerate of others are reckless drivers who pay no attention to traffic regulations.
Answer: No S is P -> No P is S.
No reckless drivers are people who are considerate of others.
2. All graduates of West Point are commissioned officers in the U.S. Army.
Answer: All S is P -> Some P is S.
Some commissioned officers are graduates.
3. Some European cars are overpriced and underpowered automobiles.
Answer: Some S are P -> Some P is S.
Some overpriced and underpowered automobiles are European cars.
4. No reptiles are warm-blooded animals.
Answer: No S is P -> No P is S.
No warm-blooded animals are reptiles.
5. Some professional wrestlers are elderly persons who are incapable of doing an honest day’s work.
Answer: Some S is P -> Some P is S.
Some elderly persons are professional wrestlers.
EXERCISE B INSTRUCTIONS
State the obverses of the following propositions:
PROBLEMS
1. Some college athletes are professionals.
Answer: Are non-professionals.
2. No organic compounds are metals.
Answer: Are non-metals.
3. Some clergy are not abstainers.
Answer: Not non-abstainers.
4. No geniuses are conformists.
Answer: Are non-conformist.
5. All objects suitable for boat anchors are objects that weigh at least fifteen pounds.
Answer: Are non-objects that weigh at least fifteen pounds.
EXERCISE C INSTRUCTIONS
State the contrapositives of the following propositions and indicate which of them are equivalent to the given propositions.
PROBLEMS
1. All journalists are pessimists.