Inductive/Dedu ctive Reasoning Using reasoning in math and science.

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Inductive/Dedu ctive Reasoning Using reasoning in math and science

Inductive Reasoning  Process of reasoning that a rule or statement is true based on a pattern.  You can draw a conclusion from a pattern called a Conjecture.  A Conjecture is a statement you believe to be true based on inductive reasoning.

Example  The product of an even number and an odd number is _______  List some examples and look for a pattern  2(3)= 62(5)=10 4(3)=12  Product of even and odd number is ____

Counterexample  To show a conjecture is always true, you have to prove it.  To show that a conjecture is false, you only have to find one example in which the conjecture isn’t true.  This is called the Counterexample

Examples  Every pair of supplementary angles includes one obtuse angle.  Is there a counterexample that disproves this statement?

Conditional Statements  Can be written in the form p  q  An “if then” statements  The Hypothesis is followed by “if”  The conclusion is followed by “then”

Example  Hypothesis: A number is an integer. It is a natural number.  If a number is an integer, Then it is a natural number.  Analyze the truth value of the statement.  Is the hypothesis always true?  Can you find a counterexample to disprove it?

Related Conditionals Hypothesis – P  q Converse- flipping hypothesis and conclusion q  p Inverse- Negate the hypothesis and conclusion -p  -q Contrapositive – switch and negate hypothesis and conclusion -q  -p

Truth Value  Need to test the truth value of all statements.  Example:  If I have a cold then I am sick.  If I’m sick then I have a cold  If I don’t have a cold then I’m not sick  If I’m not sick then I don’t have a cold.