PRACTICE EXERCISE 2


1. Consider the following axiom set.

Axiom 1. Every ant has at least two paths.

Axiom 2. Every path has at least two ants.

Axiom 3. There exists at least one ant.

What are the undefined terms in this axiom set?

Answer:___________


The undefined terms are ant, path, and has.


Note: that ant and path are elements, and has is a relation since it indicates some relationship
between ant and path.


2.)Consider the following axiom set.


1. Every hive is a collection of bees.

2. Any two distinct hives have one and only one bee in common.

3. Every bee belongs to two and only two hives.

4. There are exactly four hives.

What are the undefined terms in this axiom set?
Answer: ________


2. Subject: Committees


Axiom 1: Each committee is a set of three members

Axiom 2: Each member is on exactly two committees.

Axiom 3: No two members may be together on more than one committee.

Axiom 4: There is at least one committee.

What are the Undefined terms: _______________?


3. Subject : silliness

Axiom 1: Each silly is a set of exactly three dillies

Axiom 2: There are exactly four dillies.

Axiom 3: Each dilly is contained in a silly.

Axiom 4: No dilly is contained in more than one silly.


NOTE: That in the example, the axioms defined a new term (“identity”). This isn’t an

undefined term because the axiom includes a definition. Also, these axioms refer to basic
set theory that you learned in Discrete Math. For our purposes, we will assume all of those
basic set theory terms are known. It is possible to view set theory itself as another
axiomatic system, but that is beyond the scope of this course.


What are the undefined terms in this axiom set?


Unhelpfula answer=REPORT!​