Chapter 1.7, Problem 1PSA

To determine

The Four elements found in any deductive structure.

Answer to Problem 1PSA

1. Undefined terms
2. Assumptions known as postulates.
3. Definitions.
4. Theorems and their conclusions.

Explanation of Solution

Given:

Deductive structure.

Basics of deductive structure.

• Undefined terms: The terms that are not defined or we have incomplete information about them.

E.g. A point anywhere in the space or we can say whose location is not known.

• Postulates: Postulates can be defined as an unproven assumption and states the meaning of a term.

E.g. If any line segment is divided into two congruent parts by any point, then that point would be the mid-point.

• Definitions: States the meaning of a term and are always reversible.

For example: An example of math is arithmetic, the study of addition, subtraction, multiplication and division

• Theorems and their conclusions: Theorems are the statements which require proof to derive a conclusion and are not always reversible.

For example: The "Pythagoras Theorem" proved that $a^2+b^2=c^2$ for a right-angled triangle