LESSON 3.1 Inductive and Deductive Reasoning Flashcards
What is the definition of inductive reasoning?
Inductive reasoning is the process of reasoning that arrives at a general conclusion based on the observation of specific examples.
How is inductive reasoning typically used?
Inductive reasoning is used to make conjectures or general conclusions based on observed events or examples.
What is a conjecture in the context of inductive reasoning?
A conjecture is a general conclusion drawn based on observations or specific examples, which may or may not be correct.
What is a counterexample in inductive reasoning?
A counterexample is an example that disproves a conjecture.
Give an example of a conjecture made using inductive reasoning.
If the squares of odd numbers (e.g., 3, 5, 7, 9) are all odd, we may conjecture that the square of any odd integer is odd.
What is the test for a conjecture in inductive reasoning?
To test a conjecture, we check it against additional examples or find a counterexample to disprove it.
What is the definition of deductive reasoning?
Deductive reasoning is the process of reasoning that arrives at a conclusion based on previously accepted general statements.
How does deductive reasoning differ from inductive reasoning?
Deductive reasoning relies on known truths or general statements to derive conclusions, while inductive reasoning uses specific examples to make general conclusions.
What is a common use of deductive reasoning in mathematics?
In mathematics, deductive reasoning is used to prove theorems based on axioms and previously accepted truths.
Give an example of deductive reasoning.
“Starfish are invertebrates. Patrick is a starfish. Therefore, Patrick is an invertebrate.”
Can inductive reasoning be used to prove a conjecture?
No, inductive reasoning cannot definitively prove a conjecture, but it can provide evidence or suggest that a conjecture is likely true.
How can deductive reasoning be used to prove a conjecture?
Deductive reasoning can be used to prove a conjecture by deriving conclusions logically from established general statements or axioms.
Provide an example of using deductive reasoning to prove a conjecture.
For the conjecture that multiplying a number by 3, adding 6, dividing by 3, and subtracting the original number always results in 2, deductive reasoning shows that the final result is always 2 for any starting number.
What is the result when you follow the steps of the conjecture involving multiplication by 3, adding 6, dividing by 3, and subtracting the original number?
The result is always 2, regardless of the number chosen initially.
What role do axioms play in deductive reasoning?
Axioms serve as foundational truths from which further conclusions (theorems) are logically derived using deductive reasoning.
