Sprint 4.1: Deduction And Induction

Scenario 1: "All noble gases are stable. Helium is a noble gas. Therefore, helium is stable." Here, the reasoning moves from a general rule to a specific conclusion, meaning this is an example of . Scenario 2: "Every time we heat this metal in the lab, it expands, so all metals expand when heated." Because the logic builds from specific observations to a broad general rule, we are using . Scenario 3: "The patient has a high fever and joint pain, so Dengue is the most likely cause." This reasoning forms the best explanation from incomplete evidence to a probable hypothesis, which defines .

In Euclid's geometry, foundational truths that are accepted without proof are known as , which serve as the starting point for further logical deduction. A classic Aristotelian logical argument consisting of a major premise, a minor premise, and a conclusion is called a . After proving a major mathematical theorem, a proposition that follows naturally and requires little or no additional proof is termed a . In formal logic, a statement that is unconditionally true in every possible interpretation, such as 'It will rain or it will not rain,' is recognized as a . Scientific observation often relies on reasoning, where specific instances and data points are gathered to form a broader, generalized theory.