Assume the following axioms. undefined terms: point, line, contain, lie on Axiom 1. There are at least three points. Axiom 2. Each line contains at least 2 points. Axiom 3. Each point lies on exactly two distinct lines. Determine whether Statement 1 is consistent or inconsistent with the first three axioms. Then, determine whether Statement 2 is independent or dependent from the first three axioms. Briefly justify your answers. Statement 1. There exists a point that is on a single line only. Statement 2. There are at least three lines.

Assume the following axioms. undefined terms: point, line, contain, lie on Axiom 1. There are at least three points. Axiom 2. Each line contains at least 2 points. Axiom 3. Each point lies on exactly two distinct lines. Determine whether Statement 1 is consistent or inconsistent with the first three axioms. Then, determine whether Statement 2 is independent or dependent from the first three axioms. Briefly justify your answers. Statement 1. There exists a point that is on a single line only. Statement 2. There are at least three lines.

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.2: Statements And Reasoning

Problem 56E: In Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of...

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