Problem Solving
Inductive and Deductive
Reasoning

Inductive Reasoning
The process of reaching a general conclusion by
examining specific examples.
Conjecture -
The conclusion formed by using
inductive reasoning.

Example:
Use inductive reasoning to predict the next number
in each of the following lists.
a.
3, 6, 9, 12, 15, ?
b.
1, 3, 6, 10, 15, ?
Answer:
a.
18
b.
21

Exercise:
Use inductive reasoning to predict the next number in each of the
following lists.
a.
5, 10, 15, 20, 25, ?
b.
2, 5, 10, 17, 26, ?
Use Inductive Reasoning to Make a Conjecture:
Consider the following procedure: Pick a number. Multiply the
number by 8, add 6 to the product, divide the sum by 2, and
subtract 3. Complete the above procedure for several different
numbers. Use inductive reasoning to make a conjecture about the
relationship between the size of the resulting number and the size
of the original number.

Counterexamples
A statement is a true statement provided that it is true in all cases. If
you can find
one case
for which a statement is not true, called a
counterexample
, then the statement is a false

Verify that each of the following statements is a false statement by
finding a counterexample. For all numbers
x
:
a. I x I > 0
b. x^2 > x
c. X^
2 ^ 1/2
Solution

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- Winter '17