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 axiomsfor 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, excellentpersonAxiom 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. BRIEFLYjustify 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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Answered: A. Consider the axiomatic system as…

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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Hi, We are learning about Logic and Axiomatic Systems. I have trouble: Identifying which statements are simple statement, and compound statement, and why? And what are the connectives involved if a statement is a compound statement? Here are the given statements: Statement 1: Both players start at the same time. Statement 2: Each player decides which of the seven houses in his control he wishes to begin with. Statement 3: He/she picks up all of the shells from his chosen hole, and moves his hand around the board in a clockwise-direction, dropping one shell in each hole or head he passes over but excluding the opponent's head. Statement 4: If the last shell on the player's hand lands on an empty house, then he/she stops and wait for the next turn. Please help me. Thank you!
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Directions: Translate each argument into symbolic form (using the suggested letters) and determine whether the argument is valid or invalid by using truth table (Method 1) or standard form of arguments (Method 2). State your answer in sentence form. He is dumb or lazy. (D, L) He is dumb. Therefore, he is not lazy.
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