Unit One Lesson Two Notes
In lesson two, we learned about inductive and deductive reasoning as well as conjectures. Conjectures are statements that are true based on reasoning. Inductive reasoning is the process of proving something true because other specific cases are true. Deductive reasoning is the process of proving definitions, rules, and statements true based on logic. Just because a statement is a conjecture doesn't mean that it is true. Conjectures can be disproven by using a counterexample. Counterexamples are simply examples that prove conjectures wrong. For example, you can start with the conjecture, "Only ducks have bills.". We can prove this wrong by giving the example that geese are not ducks, but they also have bills. Because geese do have bills, we can make a counterexample disproving the statement, "Only ducks have bills." There are many ways of making conjectures, such as finding a pattern, applying real numbers, and drawing pictures.