Reasoning Strategies
Goal:
• To be able to identify a deductive or
inductive reasoning strategy
• State the hypothesis and conclusion of
deductive statements
• Write a converse
• Show a conterexample
Inductive Reasoning
• Conclusions based
on observations
and patterns
• “Conjecture”
• “Counterexample”
will show a
conjecture is false
Logic
Deductive Reasoning
• Conclusion based
on facts
• “If… then…”
“1” if Inductive Reasoning
“2” if Deductive Reasoning
1
For the past two weeks there have always
been an even number of birds at your feeder.
Today there will be an even number of birds
at your feeder.
“1” if Inductive Reasoning
“2” if Deductive Reasoning
1
In the last week, whenever you walked out
your door and saw your cat in the tree, it
rained that afternoon. You saw your cat in the
tree this morning. It will rain this afternoon.
“1” if Inductive Reasoning
“2” if Deductive Reasoning
2
The sum of two odd numbers is always an
even number. The sum of 17 and 21 is even.
“1” if Inductive Reasoning
“2” if Deductive Reasoning
1
The last 10 times you pushed an oddnumbered button, a red light flashed. If you
push the button “5”, a red light will flash.
“1” if Inductive Reasoning
“2” if Deductive Reasoning
2
If yesterday was Thursday, then tomorrow is
Saturday.
If yesterday was Thursday,
then tomorrow is Saturday.
Hypothesis
Conclusion
If tomorrow is Saturday,
then yesterday was Thursday
Converse
Converse
• The converse of a conditional statement can
be found by interchanging the hypothesis
and conclusion.
• The converse of a conditional statement
may or may not be true
Counterexample
• One statement that proves the statement to
be false
• All you need is one counterexample to
prove something false
Is the converse true (touch your
lips) or false (touch nose)
If a number is divisible by two,
then it is an even number
Is the converse true (touch your lips)
or false (touch nose)
If x = 5, then x2 = 25
-5
If false, give a counterexample.
Is the converse true (touch your lips)
or false (touch nose)
If a figure is a square, then
it has 4 sides.
Rectangle
If false, give a counterexample.
Which is a counterexample to the conjecture
If a>b and c>d,
then ac > bd
1
2
3
4
There is no counterexample. The
conjecture is true.
Give a counterexample to the conjecture:
The difference of two rational
numbers is always less than at
least one of the numbers.
(for example, the difference of 9 and 2 is 7)
8 and -5
8   5  13
If it is not raining, Jack will walk the dog.
If it is not raining, Jerry will go swimming.
If it is not raining, Jerry will go swimming.
Assignment
Page 192 (1-5) all and Page 193 (1-5) all