2.2 :Deductive Reasoning
Objectives:
1. To use deductive
reasoning to prove a
conjecture is true
Assignment:
• P. 22: 15-19
• P. 24: 11-19
Objective 1
You will be able
to use deductive
reasoning to
prove a
conjecture
is true
Exercise 1
Numbers such as 3, 4, and 5 are
consecutive integers. Make and test a
conjecture about the sum of any three
consecutive integers.
History
When the architects designed
this school building, they
were approached by an
ancient secret society whose
members make up numerous
Texas dignitaries. They
convinced the architects to
add several secret passages
and hidden conference rooms
to their design plans.
History
Sometimes when I stay
after school late into
the evening grading
papers, planning
lessons, and contacting
parents, I hear strange
and inauspicious
sounds emanating from
behind one of my walls.
Conspiracy?
Thus, it is my conjecture that one of the secret
society's hidden passages lies between the
walls of Room D202 and D204. This is a bold
and perhaps conspiratorial conjecture, but I
am confident that it is true. (You should hear
the sounds--Oh, my!)
Stop Making Fun of Me!
I have told few people of
my theory, and they
unanimously dismiss
my conviction with
ridicule. (Then they
ask me if I frequently
watch re-runs of the XFiles with the notion
that the story lines are
largely nonfiction!)
Redemption
To convince the skeptics and to redeem my
reputation, I need absolute and conclusive
proof that there exists a hidden passage
between these classrooms.
Proof
The Principle of
Laplace:
The weight of
evidence for an
extraordinary claim
must be
proportional to its
strangeness.
In Other Words…
“Extraordinary claims
require
extraordinary
evidence.”
-Carl Sagan
Exercise 2
In your group, come up with a nondestructive
method for proving or disproving the
extraordinary claim that there’s a secret
tunnel between D202 and D204.
Exercise 3
In the Sudoku
puzzle shown,
what number
must be written
in the blue box?
Why?
?
Deductive Reasoning
The process of
demonstrating that
if certain statements
are accepted as
true, then other
statements can be
shown to follow
from them.
Deductive Reasoning
The “accepted” statements are sometimes
premises or assumptions, and all
deductive arguments must have them.
Deductive reasoning uses logical inference
to build on these assumptions.
Unlike inductive reasoning, deductive
reasoning will always lead to the truth
as long as the assumptions are true.
Exercise 4
All humans have
skeletons is a
reasonable
assumption. So,
since Mr. Noel is a
human, what must
be true about him?
Inductive Reasoning
Deductive Reasoning
Inductive vs. Deductive
1. We use inductive reasoning to investigate
and discover things about our world.
2. Since the conjectures we make using our
inductive reasoning is based on our fallible
observation skills, we can be wrong.
3. We can search for a counterexample to
disprove our conjectures.
4. In mathematics, we use our deductive
reasoning to prove our conjectures beyond
all uncertainty.
2.2 :Deductive Reasoning
Objectives:
1. To use deductive
reasoning to prove a
conjecture is true
Assignment:
• P. 22: 15-19
• P. 24: 11-19