Chapter 2: Deductive Reasoning. -The process of reasoning from one or more general statements to reach a logically certain conclusion.

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Presentation transcript:

Chapter 2: Deductive Reasoning

-The process of reasoning from one or more general statements to reach a logically certain conclusion

Example of Deductive Reasoning fvL4 fvL4

2-1: If-then Statements; Converses If-then Statements/ Conditional Statements/ Conditionals (all same thing) If p, then q Hypothesis, conclusion

Examples 1.) If it rains after School, I will give you a ride home.

Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC

Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC 3.) If I got 100% on my test, then I got an A.

Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC 3.) If I got 100% on my test, then I got an A. Are either True or False

Examples 1.) If it rains after School, I will give you a ride home. 2.) If B is between A and C, then AB + BC = AC 3.) If I got 100% on my test, then I got an A. Are either True or False – If False, provide a counterexample If only false once, then the whole statement is still false

Example: If a # is a rational #, it is an integer

– False: ¾ – There are many true examples, but all you need is one false to make it false

Example: If a # is a rational #, it is an integer – False: ¾ – There are many true examples, but all you need is one false to make it false Example: If a is positive, then a > -b

Example: If a # is a rational #, it is an integer – False: ¾ – There are many true examples, but all you need is one false to make it false Example: If a is positive, then a > -b – False: a = 3, b = -4

Converse -interchanging the hypothesis and conclusion -If q, then p

Converse -interchanging the hypothesis and conclusion -If q, then p Converse of previous examples 1.) If I gave you a ride after school, then it rained 2.) IF AB + BC = AC, then B is between A and C 3.) If I got an A on the test, then I got 100%.

If 4x = 20, then x = 5. Is the converse true?

Biconditional If statement and converse are both true,, then it is called a biconditional – You can then use the words if and only if (iff) – 4x = 20 if and only if x = 5

Biconditional If statement and converse are both true, then it is called a biconditional – You can then use the words if and only if (iff) – 4x = 20 if and only if x = 5 Every definition can be written as a biconditional – Ex: Congrent segments are segments that have equal lengths – Converse: Segements that have equal lengths are congruent segments

Your Turn Come up with 3 examples 1.True conditional, false converse 2.False conditional 3.Biconditional

Other ways to write conditionals If p, then q P implies q P only if q q if p All the same thing!

Classwork Pg 34: 1, 4, 8, 10, 14

Homework: Pg 35: 1-31 odd