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A. Consider the axiomatic system as described. Axiom1: There are exactly three pins. Axiom2: Every pins is on atleast two lines. Axiom 3: Each line passes through at most two pins. 1. Identify the undefined terms and the undefined relations in the axiomatic system. For Items 2 and 3, explain why the given propositions cannot be considered as additional axioms for the system. Note that an axiomatic system should be consistent and independent. 2. "There are exactly two lines." Why cannot this proposition be an additional axiom in the given system? 3. "There are at least three lines." Why cannot this proposition be an additional axiom in the given system?

A. Consider the axiomatic system as described. Axiom1: There are exactly three pins. Axiom2: Every pins is on atleast two lines. Axiom 3: Each line passes through at most two pins. 1. Identify the undefined terms and the undefined relations in the axiomatic system. For Items 2 and 3, explain why the given propositions cannot be considered as additional axioms for the system. Note that an axiomatic system should be consistent and independent. 2. "There are exactly two lines." Why cannot this proposition be an additional axiom in the given system? 3. "There are at least three lines." Why cannot this proposition be an additional axiom in the given system?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A. Consider the axiomatic system as described. Axiom1: There are exactly three pins. Axiom2: Every pins is on atleast two lines. Axiom 3: Each line passes through at most two pins. 1. Identify the undefined terms and the undefined relations in the axiomatic system. For Items 2 and 3, explain why the given propositions cannot be considered as additional axioms for the system. Note that an axiomatic system should be consistent and independent. 2. "There are exactly two lines." Why cannot this proposition be an additional axiom in the given system? 3. "There are at least three lines." Why cannot this proposition be an additional axiom in the given system? B. Consider a ABC Student Axiomatic System as described. undefined terms: ABC student, scholarly person, intelligent person, honorable person, excellent person Axiom 1: All ABC students are intelligent persons. Axiom2: Some ABC students are honorable persons. Axiom 3: All intelligent persons are scholarly persons. Axiom 4: Excellent persons are all and only those intelligent persons that are honorable. Identify whether the following propositions are TRUE or FALSE based on the axioms. BRIEFLY justify your answer. 1. Some honorable persons are scholarly persons. 2. All excellent persons are scholarly persons. 3. All intelligent persons are excellent persons. 4. Some scholarly persons are excellent persons. 5. Some intelligent persons are not scholarly persons.
Transcribed Image Text:A. Consider the axiomatic system as described. Axiom1: There are exactly three pins. Axiom2: Every pins is on atleast two lines. Axiom 3: Each line passes through at most two pins. 1. Identify the undefined terms and the undefined relations in the axiomatic system. For Items 2 and 3, explain why the given propositions cannot be considered as additional axioms for the system. Note that an axiomatic system should be consistent and independent. 2. "There are exactly two lines." Why cannot this proposition be an additional axiom in the given system? 3. "There are at least three lines." Why cannot this proposition be an additional axiom in the given system? B. Consider a ABC Student Axiomatic System as described. undefined terms: ABC student, scholarly person, intelligent person, honorable person, excellent person Axiom 1: All ABC students are intelligent persons. Axiom2: Some ABC students are honorable persons. Axiom 3: All intelligent persons are scholarly persons. Axiom 4: Excellent persons are all and only those intelligent persons that are honorable. Identify whether the following propositions are TRUE or FALSE based on the axioms. BRIEFLY justify your answer. 1. Some honorable persons are scholarly persons. 2. All excellent persons are scholarly persons. 3. All intelligent persons are excellent persons. 4. Some scholarly persons are excellent persons. 5. Some intelligent persons are not scholarly persons.
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