2.1 Inductive Reasoning
Conjecture: an unproven statement based on observation
Inductive Reasoning: a conjecture for a general case. (Making a conclusion based on observations)
Ex: Based on the pattern, what will the next three numbers be?
a) 1,5,9,13,...
b) 2,6,18,...
c)10,5,2.5,...
Ex: What do you suspect the next two figures in the pattern would be?
a.) ♣♦♥♠♣♦
b.
* To show that a conjecture is true, you must show that it works in all cases. To show that a conjecture is false, you
need to find only one way that it doesn’t work.
Counterexample: a specific case that shows that is used to prove a conjecture is false
Ex:
Conjecture: A polygon with four sides is a square.
Counterexample: ____________________________________________
Ex:
2
Conjecture: The value of x is always greater than x.
Counterexample: _____________________________________________
Ex:
Conjecture: Two supplementary angles are each 90°!
Counterexample: _____________________________________________
1