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

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Tarski World a g. Using the following predicates: square (x) is true if x is a square (otherwise it is false) star(x) is true if x is a star (otherwise it is false) circ(x) is true if x is a circle (otherwise it is false) shade (x) is true if x is shaded (otherwise it is false) next.to(x, y) is true if x and y are adjacent horizontally, vertically or diagonally. This relation is not reflexive for any object. For each of the statements below, determine whether the statement is true or false. You need not justify your response. 3xcirc(x) A shade(xr) Va shade(r) V ¬shade(r) Va square(r) → ¬shade(r) Vævy(star(r) A ¬shade(r) A next.to(x, y) → shade(y) ^ circ(y)) vr next.to(x, y) A shade(r) 3rvy next.to(r, y) A shade(r)
Predicates P, T and E are defined below. The domain is the set of all positive integers. P(x) : x is even T(x, y): 2 = y E(x, y, z): x³ = z Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its truth value. Logical Expression: (h) T(5, 16) → E(6, 3, 36) *Create a truth table for the expression
Consider the axiomatic system below with cat, scratch, and pole as undefined terms. Any two cats scratch exactly one pole. There are exactly four cats. • Every pole is scratched by exactly two cats. • There are exactly five poles. Show that this axiomatic system is inconsistent.
ii. Let F(x,y) be the open sentence "x can fool y" where the domain of discourse is the set of all people in the world. Express each of these statements using logical quantifiers. c. Everybody can fool somebody. e. Everyone can be fooled by somebody. f. There is somebody who can be fooled by everybody.
Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y
I need help in this Discrete Mathemathics Question based on the Consistent System Specs. This is the statement- The student either has undergraduate courses or post-graduate courses, but not both. The student does not have undergraduate courses unless he does not have a bachelor’s degree. The student has a bachelor’s degree only if he has post-graduate courses. The student has undergraduate courses. I need help in determining whether the given specification is consistent or not using Rules of Logical Equivalences.
Philosophy math Problem b
GOOD DAY! THIS IS ALL ABOUT THE SUBJECT DISCRETE MATHEMATICS.... AND THE TOPIC IS ALL ABOUT LOGIC OPERATORS. PLEASE ANSWER ONLY PART I. number 1-4 please PLEASE SEND YOUR SOLUTION ALSO PLEASE
Determine whether the given specification is consistent or not. 1. The student either has undergraduate courses or post-graduate courses, but not both. The student does not have undergraduate courses unless he does not have a bachelor's degree. The student has a bachelor's degree only if he has post-graduate courses. The student has undergraduate courses. a. Translation: b. Solution using Rules of Logical Equivalences:
b) Determine if the statement below is true or false, and explain your reasoning. If two statements are logically equivalent, then so are their negations.

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