Inductive and Deductive Reasoning
What are inductive and deductive reasoning?
Inductive reasoning is the process of reasoning that a statement is true because specific cases, patterns or examples are true.
Deductive reasoning is the process of reasoning that a statement is true by logic or fact.
Identify the hypothesis and conclusion of the conditional statement. If I answer a phone call, then I have a phone.
The hypothesis is if I answer a phone call. The conclusion is then I have a phone.
Determine if the conjecture is valid by the Law of Detachment. Given: If Sue buys a TV, then Sue must have money. Sue has money. Conjecture: Sue bought a TV.
Invalid.
Give a counterexample to the following statement.
If you sneeze, then you must be sick.
ex) You may have an allergy.
I have only seen grey mice in my life. Therefore all mice are grey.
Inductive reasoning.
Write a conditional statement from the following fact. A dog has fur.
If it is a dog, then it has fur.
Determine if the conjecture is valid by the Law of Syllogism. Given: If you are in Lansing, then you are in Michigan. If you are in Michigan, then you are in the USA. Conjecture: If you are in Lansing, then you are in the USA.
Valid
Give a counterexample to the following statement.
If you are tired, then you ran 5 miles.
ex) I may be tired because I didn't sleep last night.
Determine whether the following statements are an example of deductive or inductive reasoning. Dogs have fur, and Fido is a dog. Therefore, Fido has fur.
Deductive reasoning
Write the definition as a biconditional. An acute angle is an angle whose measure is less than 90 degrees.
It is an acute angle if and only if its measure is less than 90 degrees.
Determine whether the conjecture is valid by the Law of Detachment. Given: If Nancy makes dinner, then Nancy must have food. Nancy makes dinner. Conjecture: Nancy has food.
Valid.
Give a counterexample to the following statement.
If a figure has four right angles, then it is a square.
It could be a rectangle.
Write the Converse of the given conditional. Then state the truth value of the Conditional and of the Converse.
If two angles are supplementary, then the angles have a sum of 180 degrees.
Converse: If two angles have a sum of 180 degrees, then they are supplementary.
Both the conditional and the converse are True.
Give a counterexample to the following statement.
If you are in Geometry, then you have Ms. Hodik.
You may have a different Geometry teacher, like Ms. Brazil or Mr. Stanton...
There is a myth that walking under a ladder is bad luck. A group of scientists observed a person who had stepped under a ladder. They found the person had good luck since he won the lottery and concluded the myth was false. Why is this an example of inductive reasoning?
It is inductive reasoning beacause it is based on observations.
Write the converse and biconditional for the following conditional statement.
If two angles are complementary, then their sum is 90 degrees.
Converse: If the sum of two angles is 90 degrees, then they are complementary.
Biconditional: Two angles are complementary if and only if their sum is 90 degrees.
Describe what a counterexample is.
An example that proves a conditional statement is false (not always true).