Download 1.4 Proving Conjectures: Deductive Reasoning

Name: ______________________
Date: ________________
Foundations of Mathematics 11
Chapter 1- Inductive and Deductive Reasoning
1.4 Proving Conjectures: Deductive Reasoning
Today’s Goal: To prove mathematical statements using a logical argument.
Deductive reasoning: __________________________________________________
__________________________________________________
Mathematical Proof
Proof: __________________________________________________
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Conjecture: The sum of two odd numbers will always be even.
Prove it!
Conjecture: The Square of an even number is always even.
Proof:
Conjecture: If I add three consecutive integers, the sum will always be three times the
median of the numbers (the middle number).
Supporting examples:
(inductive reasoning)
1+2+3=6 and 3(2)=6
3+4+5=12 and 3(4)=12
Proof (deductive reasoning): Let x represent the median of any three consecutive
integers.
Use deductive reasoning to come to a conclusion:
Your turn:
1. students are teenagers. Lynn is a student.
Conclusion: Lynn is ______________________________.
2. The sum of the angles in any triangle is 180°. In ABC,  A = 90°,
therefore, B +  C = …
3. Bahamas, Barbados, Jamaica and Trinidad and Tobago are four countries in the
Caribbean. All the following statements about their land areas are true. List the
countries in order of increasing size.
i. Barbados is smaller than Trinidad and Tobago
ii. Bahamas is neither the largest nor the smallest.
iii. At least two countries are larger than Trinidad and Tobago.
Lastly, explain whether the conclusion follows logically from the given statement.
Cars produce carbon dioxide gas. Carbon dioxide gas contributes to the depletion of the
ozone layer. Therefore, if there were no cars, the ozone layer would not be depleted.
Example: Explain how the transitive property is used in this two-column proof.
Assignment: p. 31 # 2 – 8, 10, 13