Axiomatic Structure of Mathematical Systems

What condition exists if an axiomatic system is independent?

• It can be proven from the other axioms.

• It cannot be proven from the other axioms.

• It is true based on the other axioms.

• It is false based on the other axioms.

What is the illustration to define the undefined terms so that the axioms are true?

• Model

• Replica

• Isometry

• Diagram

What is any statement that can be proven using logical deduction from the axioms?

• Undefined Terms

• Definition

• Theorem

• Axiom

What is a list of undefined terms together with a list of axioms (presupposed to be “true”), a definition in proving theorems and other components of mathematical system?

• Mathematical Structure

• Mathematical Set

• Axiomatic Structure

• Axiomatic Set

What condition exists if an axiomatic system is complete?

• If every true statement can be proven from the axioms.

• If every true statement exists.

• If every true statement can stand on its own.

• If every true statement is independent and consistent.

What condition exists if an axiomatic system is consistent?

• It can be proven from the other axioms.

• It cannot be proven from the other axioms.

• There is a model for an axiomatic system where the axioms are all true .

• There is a model for an axiomatic system where one axiom is independent.

How many models can be used to illustrate axiomatic systems?

• Only one

• Two models

• Three models

• Cannot be determined

What is an axiom?

• presupposed to be “true”

• always true

• presupposed to be “false”

• always false

Which of the following axioms cannot be proven from other presupposed axioms?

• Consistent

• Redundant

• Independent

• Inconsistent

Which axiom satisfies the model below?

• Each pot is a set of two flowers.

• Each flower is on exactly one pot.

• Two flowers may be together on more than one pot.

• There is at least one flower.