Chapter 2Reasoning and Proofs

Chapter 2 Glossary Terms

Conjecture Inductive Reasoning Counter Examples Statement Truth Value Negation Compound

Statement Conjunction Disjunction Truth Table

Hypothesis Conclusion Converse Inverse Contrapositive Deductive Reasoning Postulate Axiom Theorem Proof

"Have some fire. Be unstoppable. Be a force of nature!" Cristina Yang

2.1 Inductive Reasoning and Conjecture

Objective: Define Inductive reasoning and practice developing conjectures and finding counter examples

Check.1.6 , Use inductive reasoning to write conjectures and/or conditional statements.

Check.4.18 Use counterexamples, when appropriate, to disprove a statement.

CLE 3108.1.3 , Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.

Inductive reasoning - Glossary

Making generalizations about the environment as a whole, based on a necessarily limited number of observations.

Inductive reasoning is reasoning that is based on patterns you observe.

In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative conjectures that we can explore, and finally end up developing some general conclusions or theories.

Conjecture

A mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic.

Patterns

Pattern

2, 4, 12, 48, 240, ___, ____

Algebraic and Geometric Conjectures

A. Make a conjecture about the sum of an odd number and an even number. List some examples that support your conjecture.

Step 1 List some examples.

1 + 2 = 3 1 + 4 = 5 4 + 5 = 9 5 + 6 = 11

Step 2 Look for a pattern.

Notice that the sums 3, 5, 9, and 11 are all

odd numbers.Step 3 Make a conjecture.

Answer: The sum of an odd number and an even number is odd.

Geometric Conjecture

For points L, M and NLM = 20, MN = 6, LN = 14

Make a conjecture and draw your figureL MN

14 6

20

L, M, and N are collinear

Given: ACE is a right triangle with AC = CE. Which figure would illustrate the following conjecture? ΔACE is isosceles, C is a right angle, and is the hypotenuse.

A. B.

C. D.

Find Counterexamples

UNEMPLOYMENT Based on the table showing unemployment rates for various counties in Texas, find a counterexample for the following statement. The unemployment rate is highest in the cities with the most people.

Practice Assignment

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