Transcript 2.1 Use Inductive Reasoning

2.1 Inductive Reasoning
Inductive Reasoning: is the
process of forming a conjecture
based on a set of observations
Conjecture is a statement that is believed to be true but not yet
proved.
Ex. 1 Use inductive reasoning to
form a conjecture
1, 2, 3, 4, 5, 6, 7, ….
*Purple is your given
*Green is your guess of what comes next
Conjecture
The sequence increases by one each time
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Ex. 2 Inductive Reasoning
5, 10, 15, 20, 25, 30, 35, 40, 45, ….
Conjecture 1: The sequence goes up by five
each time.
Conjecture 2: ends in a 5, then a 0, then a 5,
and so on…and all the numbers
in the tens place appear twice in
the sequence.
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Ex. 3
Inductive Reasoning
Conjecture 1: every term in the sequence is
rotated counterclockwise 90 degrees.
Conjecture 2: continuously repeats the four
positions of right, bottom, left, top, right,
bottom, left, top, …
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Ex 4
Describe how to sketch the fourth figure
in the pattern. Then sketch the fourth
figure.
Conjecture: ??
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EXAMPLE I
Describe the pattern in the numbers
–7, –21, –63, –189,… and write the next
three numbers in the pattern.
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EXAMPLE II
Numbers such as 3, 4, and 5 are called
consecutive integers. Make and test a
conjecture about the sum of any three
consecutive integers using inductive
reasoning.
Hint: We must first gather data before we make predictions
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EXAMPLE IV
Make and test a conjecture about the
sign of the product of any three negative
integers.
Hint: We must first gather data before we make predictions
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Counterexamples in Real Life

All birds can fly.

A basketball player must be tall in order to be
good at dunking baskets.

Students with low grade-point averages in
high school do not contribute to the academic
community.
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Counterexample in Math
A counter example in math is an example
for which the conjecture is false.
* It is one number or one picture or one set of
numbers….it is NOT a written reason!!!
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EXAMPLE A – Counter Examples
Conjecture: The sum of two numbers is
always greater than the larger number.
Are they any counterexamples that exist to disprove this
conjecture?
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EXAMPLE V – Counter Examples
Find a counterexample to show that the following
conjecture is false.
2
Conjecture: The value of x is
always greater than the value of x.
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2.3 Apply Deductive
Reasoning
Deductive Reasoning uses
facts, definitions, and the laws
of logic to form a logical
argument.
Laws of Logic
Law of Detachment
If the hypothesis of a
conditional statement
is true, then the
conclusion is also
true.
Law of Syllogism
If A, then B.
If B, then C.
If A, then C
Ex
Ex.
2. 1
Ex. Mary
1 If two
segments
have the
Ex.2
goes
to the movies
every If Ifx2Rick
>25,takes
thenChemistry
x 2 >20 this year,
same
length,
then
they
are
Friday and Saturday night.
then Jesse will be Rick’s partner. If
congruent.
If x>5, then x 2 >25.
Jess is Rick’s lab partner, then
You know that BC =XY
Rick will get an A in chemistry.
Today is Friday
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Logic Puzzle (Nicknames)
Four friends: Dave, Mike, John, and Terry, are nicknamed Stick,
Batman, Atomic Head, and Feaser, but not in that order. Which friend
has which nickname?
A. John is faster than Batman but not as strong as Atomic Head.
B. Batman is stronger than Terry but slower than Feaser.
C. Dave is faster than both Stick and John, but not as strong as Batman
Strength and speed are independent qualities.
Dave
Stick
Mike
John
Terry
x
x
x
0
Batma
n
x
0
x
x
Atomic
Head
0
x
x
x
x
x
0
x
Feaser
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