Geometry / Unit 2: Reasoning and Proof
2.3 Inductive and Deductive Reasoning
Notes
Inductive reasoning looks for a pattern in examples and makes a conjecture. Deductive reasoning uses facts, definitions and logic to reach a certain conclusion.
- A conjecture from a pattern might be false; one counterexample disproves it.
- Law of Detachment: if $p \to q$ is true and $p$ is true, then $q$ is true.
- Law of Syllogism: if $p \to q$ and $q \to r$ are true, then $p \to r$ is true.
- Example: "If it rains, the game is canceled." It rains. So the game is canceled (Detachment).
Practice
What is the next number: 3, 7, 11, 15, ...?
The pattern adds 4 each time.
"If a figure is a square, then it is a rectangle." "If a figure is a rectangle, then it has four right angles." What follows by the Law of Syllogism?
Chain $p \to q$ and $q \to r$ into $p \to r$.
"If you score over 90, you get an A." Maya got an A. What can you conclude?
Knowing the conclusion is true does not prove the hypothesis. That would be assuming the converse.
Ready for more? Take the Unit 2 test.