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Foundations of Mathematics 11
Lesson 1.3 – Proving Conjectures: Deductive Reasoning
Goal - Prove mathematical statements using a logical argument.
So far, we have been using inductive reasoning: Our conjectures come from using
specific examples!
Question – How can the conjecture “All teens like music” be supported
inductively? ___________________________________________
Proof
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Deductive Reasoning
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Deductive reasoning does not use specific examples, but rather relationships
known to be true.
Note: To prove mathematical statements, it is still important to think about
particular examples.
Ex. 1 Prove that the sum of two
even numbers is always even.
Important Definitions
Even Number
Odd Number
Ex. 2 Prove that the product of two
odd integers is always odd.
Ex. 3 Prove that the difference
between consecutive perfect
squares is always odd.
Try the following:
Ex. 4
Prove that the sum of two odd numbers and an even number is an even
number.
Ex 5 Prove that the product of an even integer and an odd integer is always even.
Practice: p. 15 #1ab, 2, 3, 11, 12, 13