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Lesson 1-1
Inductive and Deductive Reasoning
• Inductive Reasoning- the process of arriving at
a general conclusion based on observations of
specific examples.
• We can never be certain that these
conclusions are true.
• For this reason conclusions are called
conjectures, hypotheses, or educated guess.
• If there is just one case for which the
conjecture does not hold, then the conjecture
is false. Such a case in a counterexample.
• Inductive reasoning can help reveal patterns
about numbers.
• Identify the pattern to find the next number.
3, 12, 21, 30, 39
3, 12, 48, 192, 768
3, 4, 6, 9, 13, 18
• Sometimes you will have to look at the digits
that immediately precede it.
• 1,1,2,3,5,8,13,21,
• Deductive Reasoning – proving a specific
conclusion from one or more general
statements
• The conclusion that is proved true is called a
theorem.
• Consider the following procedure:
– Select a number. Multiply the number by 6. Add
8 to the product. Divide this sum by 2. Subtract 4
from the quotient.
– Repeat this procedure for 4 different numbers and
write a conjecture
– Represent the original number by n and use
deductive reasoning to prove the conjecture
• Assignment: 2 – 50, 52, 56 even on pg 9-11