An axiomatic system with captain, lead, and team as the undefined terms is given below. (1) Any two captains lead exactly one team. (2) There are exactly four captains. (3) Every team is led by exactly two captains. (4) There are exactly five teams. Prove that the axiomatic system is inconsistent.

An axiomatic system with captain, lead, and team as the undefined terms is given below. (1) Any two captains lead exactly one team. (2) There are exactly four captains. (3) Every team is led by exactly two captains. (4) There are exactly five teams. Prove that the axiomatic system is inconsistent.

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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Question

An axiomatic system with captain, lead, and team as the undefined terms is given below.

(1) Any two captains lead exactly one team.

(2) There are exactly four captains.

(3) Every team is led by exactly two captains.

(4) There are exactly five teams.

Prove that the axiomatic system is inconsistent.

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