Appendix 1: Proofs in Mathematics
- 1. NUMBER SYSTEMS
- 2. A POLYNOMIALS
- 3. COORDINATE GEOMETRY
- 4. LINEAR EQUATIONS IN TWO VARIABLES
- 5. INTRODUCTION TO EUCLID'S GEOMETRY
- 6. LINES AND ANGLES
- 7. TRIANGLES
- 8. QUADRILATERALS
- 9. CIRCLES
- 10. HERON'S FORMULA
- 11. SURFACE AREAS AND VOLUMES
- 12. STATISTICS
- 13. APPENDIX 1: PROOFS IN MATHEMATICS
- 14. APPENDIX 2: INTRODUCTION TO MATHEMATICAL MODELLING
A1.1 Introduction
In everyday life, we often need to prove claims—whether it's property disputes, financial records, or scientific theories. Proofs are essential in mathematics to establish the truth of statements logically.
A1.2 Mathematically Acceptable Statements
Example
Determine whether the following statements are always true, always false, or ambiguous:
- The sun sets in the west.
- There are 8 days in a week.
- It is raining here.
Exercise A1.1
- Identify whether the statements are mathematically acceptable.
- Provide counterexamples for statements that may not always be true.
A1.3 Deductive Reasoning
Deductive reasoning allows us to derive conclusions from established truths using logical steps.
A1.4 Theorems, Conjectures, and Axioms
A1.5 What is a Mathematical Proof?
Exercise A1.4
- Find counterexamples to disprove certain statements.
- Analyze proof structures step-by-step.