3._STEM_MATHEMATICS_SRB_-_Grade_12_Term_1

Page 1: Title Page

• Department of Education STEM Education National Schools of Excellence

• Student’s Resource Book Grade 12 Term 1 Science Technology Engineering Mathematics

• Grade 12 STEM Mathematics SRB

Page 2: Publication Details

• Issued free to schools by the Department of Education

• Published in 2021 by the Department of Education, Papua New Guinea

• Acknowledgement of contributors and the introduction of the STEM Curriculum for the first time in 2021.

• Mathematics as a core program in STEM Education.

Page 3: Table of Contents

• MODULE 12.1: DISCRETE MATHEMATICS

• Topics include:

  • The Foundations: Logic and Proof

  • Basic Structures: Sets, Functions, Sequences, Sums, and Matrices

Page 4: Module Introduction

• Discrete Mathematics involves individual, separated values, focusing on integers to solve problems.

• It's crucial in fields like computer science and has applications in many real-world scenarios.

• Prerequisites: Algebra, Arithmetic Operations, and Functions.

Page 5: Foundations - Logic and Proof

• Key Concepts include:

  • Propositional Logic

  • Applications of Propositional Logic

  • Understanding Proofs

• Familiarity with terms like Logical Operators, Mathematical Proof, Conjecture, etc., is essential.

Page 6: Background Information

• Logic is the foundation of mathematical reasoning, essential for various fields, such as computer science and programming.

• Proofs are important for establishing the correctness of mathematical statements.

Page 7: Propositions

• Propositions are declarative sentences that can be true or false.

• Examples of propositions given and definitions of propositional variables.

Page 8: Negation of Propositions

• The negation operator is introduced with a truth table layout showing the outcome of negating a proposition.

Page 9: Conjunction Operator

• Defined conjunction using logical operators with truth values detailed in a truth table format.

• Example provided helps illustrate how conjunction determines the truth of combined statements.

Page 10: Disjunction Operator

• Defined disjunction with associated truth table. Examples clarify the use of inclusive and exclusive 'or'.

Page 11: Exclusive Or Operator

• Definition and truth table presented for clarity, including discussions about when conditions are true or false.

Page 12: Conditional Statements

• Defined conditional statements, with examples showing their structure and truth values using a truth table.

Page 13: Converse, Contrapositive, and Inverse

• Definitions for each type of conditional statement provided with examples.

Page 14: Biconditional Statements

• Defined with examples explaining their truth values and conditions for being true.

Page 15: Truth Tables for Compound Propositions

• Example constructed to demonstrate how truth values of complex statements can be determined.

Page 16: Precedence of Logical Operators

• Discussion on the order of operations and how logical operators interact within statements.

Page 17: Logical Operators and Bit Operations

• Introduction to bits and how they correspond to logical truth values; explanation of how bits manipulate information.

Page 18: Exercises on Propositional Logic

• Exercises posed challenge students to apply propositional logic to analyze statements and construct counterexamples.

Page 19: More Exercises and Applications

• Additional practice exercises address different levels of complexity, challenging students to create statements with logical connectives.

Page 20: More Logical Expressions and Queries

• Exercises and problems focused on translating between logical expressions and English sentences, enhancing comprehension.

Page 21: Advanced Logic and Bitwise Operations

• Introduction to advanced concepts in logic and their applications in computing.

Page 22: Applications of Propositional Logic

• Discussion on real-world applications of logical expressions, particularly within programming and systems definitions.

Page 23: Conclusion of Applications

• Conclusion about the significance of logic in mathematics, computer