2.1 Use Inductive Reasoning
Objectives
1. To make
conjectures by
applying inductive
reasoning
2. To recognize the
limits of inductive
reasoning
Assignment:
• P. 17: 11-15
• P. 23: 1-10
• Challenge Problems
Objective 1
You will be able to
make conjectures
by applying
inductive
reasoning
Exercise 1
Use the map of
Texas provided
to make a
generalization
about the
numbering
system of
Interstate
Highways.
Exercise 1
Use the map of
the US provided
to make a
generalization
about the
numbering
system of
Interstate
Highways.
Inductive Reasoning
Inductive reasoning
is the process of
observing data,
recognizing patterns,
and making
generalizations
based on your
observations.
Inductive Reasoning
Inductive reasoning
is the process of
observing data,
recognizing patterns,
and making
generalizations
based on your
observations.
A generalization is a
statement that applies
to every member of a
group
Conjectures
in math
Hypothesis
in science
Conjecture
A conjecture is a
general, unproven
statement believed to
be true based on
investigation or
observation
Inductive Reasoning
Inductive reasoning can
be used to make
predictions about the
future based on the
past or to make
conjectures about the
past based on the
present.
Inductive Reasoning
Inductive Reasoning
Exercise 2
Numbers such as 3, 4, and 5 are
consecutive numbers. Make and test a
conjecture about the sum of any three
consecutive numbers.
Objective 2
You will be able to recognize the
limits of inductive reasoning
Whiskey Tango Foxtrot!
Exercise 3
Inductive reasoning does not always lead to the truth.
What are some famous examples of conjectures
that were later discovered to be false?
Science
Generalization
Inductive Reasoning
Experiments are used
to confirm or disprove
an hypothesis
To Prove or To Disprove
Observations
Deductive Reasoning
is used to prove
conjectures
Mathematics
Counterexamples
are used to disprove
conjectures
A single case in
which a conjecture is
not true
Exercise 4
Kenny makes the following conjecture about
the sum of two numbers. Find a
counterexample to disprove Kenny’s
conjecture.
Conjecture: The sum of two numbers is
always greater than the larger number.
Exercise 5
Prove or disprove the following conjecture:
For every integer x, x2 + x + 41 is prime.
For more information on prime numbers, visit
http://www.utm.edu/research/primes/.
2.1 Use Inductive Reasoning
Objectives
1. To make
conjectures by
applying inductive
reasoning
2. To recognize the
limits of inductive
reasoning
Assignment:
• P. 17: 11-15
• P. 23: 1-10
• Challenge Problems