Explore how conclusions are logically drawn from a set of premises using established inference rules like Modus Ponens, Modus Tollens, and the Law of Syllogism. Students will practice applying these rules to determine whether an argument’s conclusion follows logically from its premises. They will also learn to identify common logical missteps that lead to invalid inferences.
Introduction to Propositional Logic
This chapter lays the groundwork for understanding logical reasoning. Students will explore the concept of propositions, the basic building blocks of logical statements. They’ll learn how logical connectives combine propositions to form more complex statements, evaluate their truth values, and represent these values using truth tables. By the end, students will have a clear understanding of how to express and analyze simple logical statements.
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Valid Reasoning
Building on the fundamentals of logic, this chapter delves into the principles of valid reasoning. Students will study how logical inferences are drawn, ensuring arguments are sound. They’ll also explore logical equivalences, understanding how different statements can express the same truth. These lessons will equip students with the tools to analyze and construct valid arguments effectively.
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Introduction to Set Theory
This chapter introduces the foundational concepts of set theory, the mathematical study of collections of objects. Starting with the definition of sets and their basic properties, students will learn about subsets, set equality, and power sets. They’ll also explore operations on sets, such as unions, intersections, and differences. This chapter provides essential knowledge for understanding more advanced mathematical concepts.
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Proof Techniques & Set Properties – Mastering Mathematical Arguments
In this chapter, you’ll dive into the art of mathematical proofs, starting with basic proof techniques like direct proof, contradiction, and induction. You’ll also explore key properties of sets, such as De Morgan’s Laws and the distributive properties, which play a vital role in mathematical reasoning and problem-solving.
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