Inductive and Deductive Reasoning in Making Theorems, Postulates, and Axioms (Coursework Sample)

Inductive and Deductive Reasoning NP1402 (Mathematical Literacy)
Definition 1 (Reasoning). The process of thinking about something in a rational manner to draw valid conclusions.
It is a daily activity that we use to make decisions, which involves the construction of thoughts and converting them into a proposition to give reasons on why we have opted for a particular alternative over the other.
The two major types of reasoning, inductive and deductive, refer to the process by which someone creates a conclusion as well as how they believe their conclusion to be true. Mathematics and geometry in particular depend on clear thinking and logic. Deductive and inductive reasoning are tools we use to make the theorems, postulates, and axioms.
1 Inductive Reasoning
Definition 2 (Inductive Reasoning). Inductive reasoning is a method of reason- ing in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations.
Inductive reasoning is a logical approach to making inferences, or conclusions. People often use inductive reasoning informally in everyday situations.
In inductive reasoning, youstart by making observations or gathering data,take a broad view of your data and search for patterns,make general conclusions.
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☞ Inductve reasoning involves going from a series of specific cases to a general statement. The conclusion in an inductive argument is never guaranteed.
Example 1.1. Every quiz has been easy. Therefore, the test will be easy.
Example 1.2. The teacher used PowerPoint in the last few