Math 2201- Unit 1 Notes
Inductive and Deductive Reasoning
Inductive Reasoning
Reasoning from specific cases to more general cases. However, the
conclusions are UNCERTAIN.
Deductive Reasoning
Reasoning from general cases, which are known to be true, to more
specific CERTAIN conclusions .
- Please see the powerpoint handout on these two terms.
Conjecture
 A proposition which is unproven. In other words, it is a statement
which may be true or false.
 You will spend time in this unit attempting to use inductive or
deductive reasoning to show a conjecture is true. You will also use
methods to show a conjecture is false.
Examples of conjectures:
Unit 1: Inductive/Deductive Reasoning
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Mathematics Examples
Example 1
Conjecture: When adding two odd numbers, the answer is always even.
Show that this conjecture is true using inductive and deductive reasoning.
Example 2
Conjecture: The product of an odd number and an even number is always
even. Use inductive and deductive reasoning to show this is true.
Unit 1: Inductive/Deductive Reasoning
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Example 3
When adding two consecutive even integers, the answer is always even. Is
this true? If it is, use deductive reasoning to prove it.
Example 4
Develop a conjecture about the divisibility of the sum when you add three
consecutive integers. Use inductive reasoning to develop the conjecture,
and deductive reasoning to prove it is true.
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Number Tricks
Example 5
Consider the number trick below:
-
Choose any number
Multiply the number by two
Add 20
Divide by two
Subtract the number you started with
Your answer should be 10.
a) Use inductive reasoning to show this number trick likely always works
b) Use deductive reasoning to prove this number trick always works
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Example 6
Develop your own number trick, using algebra skills, and then do two examples to
check that it works.
Using Counterexamples to show conjectures are false
Proving that a conjecture is true is sometimes a difficult task. This is because you must
cover ALL cases in order to show that it is true. However, if a conjecture is a
generalization, proving it to be false is often easier.
Consider the conjecture:
The sum of the squares of two consecutive integers is always even.
How can we quickly show this is false?
Example 7
Conjecture: All fast food is unhealthy. Either prove this is true or provide a counter
example to show it’s false.
Unit 1: Inductive/Deductive Reasoning
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