2.1, 2.3, 2.4 Inductive and Deductive Reasoning and Biconditional Statements.

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2.1, 2.3, 2.4 Inductive and Deductive Reasoning and Biconditional Statements

Biconditional Statements are definitions In order for a TRUE biconditional to be created, the conditional and converse of a statement must be TRUE. Behold: Conditional: If it is a square then it has four right angles and four congruent sides. Is this true? Converse: If it has four right angles and four congruent sides then it is a square. Is this true?

Conditional: If it is a square then it has four right angles and four congruent sides. Since they are both TRUE, we have permission to write a biconditional. Here’s your rules: 1.Drop the ‘if’ and ‘then’. 2.Connect the hypothesis and conclusion with ‘if and only if’. Converse: If it has four right angles and four congruent sides then it is a square.

Let’s do it again… If it is an equilateral triangle, then all of the sides have the same measure. If all the sides have the same measure, then it is an equilateral triangle. It is an equilateral triangle if and only if all of the sides have the same measure.

♥ A biconditional is a definition. ♥ It can be read frontwards and backwards and be true. ♥ Notation: p q ♥ Abbreviation for ‘if and only if’ = iff

Reasoning based on patterns you have observed. 1. How many sides does the fifth figure of Sequence A have? 2. How many sides does the tenth figure of Sequence A have? 3. How many sides does the fourteenth figure of Sequence A have? Find the pattern: Figure # # of sides Figure # + 2 = # of sides

Generally, a guess based on past experience (inductive reasoning)

If p q is true And q r is true Then p r is true Deductive Reasoning Law of Detachment: If the hypothesis of a true conditional is true, then the conclusion is true. Let’s look in your book – pg 107. Law of Syllogism: Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement. Let’s look in your book – pg 108. If p q is true And p is true Then q is true

♥ If the conditional and converse are true, what do you have permission to make? ♥ What is the notation for a biconditional statement? ♥ Create a biconditional statement: If it is a line segment then it is a piece of a line with two endpoints. ♥ What is inductive reasoning? ♥ What is deductive reasoning? ♥ What is the Law of Detachment? ♥ What is the Law of Syllogism? ♥ What conclusion can you draw from the following statements? If it’s Monday, then it’s meatloaf. It’s Monday. ♥ What law does the previous statement demonstrate? ♥ What conclusion can you draw from the following statements? If it’s ballet, then it’s beautiful. If it’s dancing, then it’s beautiful. ♥ What law does the previous question demonstrate?

♥Your assignment ♥ pg. 87; odds pg 101; 7-29, 35-38, 43-46, all