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Below is an axiomatic system on books and shelves. Suppose we have the following axioms: A1: Every shelf is a collection of books. A2: Any two distinct shelves have one and only one book in common. A3: Every book belongs to two and only two shelves. A4: There are exactly four shelves. a. What is/are the undefined terms in the axiomatic system? b. Construct a model that will satisfy the axiomatic system. c. Prove that there are exactly six books using mathematical language. d. Is the system independent? Justify.

Below is an axiomatic system on books and shelves. Suppose we have the following axioms: A1: Every shelf is a collection of books. A2: Any two distinct shelves have one and only one book in common. A3: Every book belongs to two and only two shelves. A4: There are exactly four shelves. a. What is/are the undefined terms in the axiomatic system? b. Construct a model that will satisfy the axiomatic system. c. Prove that there are exactly six books using mathematical language. d. Is the system independent? Justify.

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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Below is an axiomatic system on books and shelves. Suppose we have the following axioms: 21. – 30. A1: Every shelf is a collection of books. A2: Any two distinct shelves have one and only one book in common. A3: Every book belongs to two and only two shelves. A4: There are exactly four shelves. a. What is/are the undefined terms in the axiomatic system? b. Construct a model that will satisfy the axiomatic system. c. Prove that there are exactly six books using mathematical language. d. Is the system independent? Justify.
Transcribed Image Text:Below is an axiomatic system on books and shelves. Suppose we have the following axioms: 21. – 30. A1: Every shelf is a collection of books. A2: Any two distinct shelves have one and only one book in common. A3: Every book belongs to two and only two shelves. A4: There are exactly four shelves. a. What is/are the undefined terms in the axiomatic system? b. Construct a model that will satisfy the axiomatic system. c. Prove that there are exactly six books using mathematical language. d. Is the system independent? Justify.
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