2.4 Deductive Reasoning - Anderson School District Five

[Pages:15]2.4 Deductive Reasoning

Inductive Reasoning: using patterns and examples to draw conclusions Deductive Reasoning: (logical reasoning) is the process of reasoning logically from given statements to a conclusion. Inductive or Deductive? Every time Kyle skips breakfast he has a head ache later that morning. Kyle makes sure to eat breakfast to prevent getting a head ache later. Marcus knows that if he seen speeding by police then he will get a speeding ticket.

1

Law of Detachment

Example 1: An auto mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins work on a car and finds the battery is dead. What conclusion can she make?

In example 1 the mechanic is using the law of detachment

Law of Detachment: If p q is true and p is true, then q is true.

A gardener knows that if it rains, the garden will be watered. It is raining. What conclusion can he make?

2

Example 1:

Using the Law of Detachment

(More difficult of the two laws)

Example 2:

If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Vladimir Nunez is a pitcher. On Monday, he pitches a complete game. What can you conclude.

3

Law of Syllogism

Law of Syllogism: allows you to state a conclusion from 2 true statements when the conclusion of one statement is the hypothesis of the other statement. If p q and q r are true statements, then p r is a true statement.

Example 1: Use the Law of Syllogism to draw a conclusion from the following true statements

If a number is prime, then it does not have repeated factors. If a number does not have repeated factors, then it is not a perfect square.

Example 2: Use the Law of Syllogism to draw a conclusion from the following true statements If a quadrilateral is a square, then it contains four right angles. If a quadrilateral contains four right angles, then it is a rectangle.

4

Example 3: If possible, state a conclusion using the Law of Syllogism. If it is not possible to use this law explain why.

a. If a number ends in 0, then it is divisible by 10. If a number is divisible by 10, then it is divisible by 5.

b. If a number ends in 6, then it is divisible by 2. If a number ends in 4, then it is divisible by 2.

5

Using Both Laws Together Example 1: Use both laws to determine a conclusion

If a river is more than 4000 mi long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 mi long.

Example 2: Use both laws to determine a conclusion The Volga River is in Europe. If a river is less than 2300 mi long, it is not one of the world's ten longest rivers. If a river is in Europe, then it is less than 2300 mi long.

6

2.5 Postulates and Paragraph Proofs

What is a postulate? What is an axiom? Theorem: a statement we can prove using

definitions, postulates and properties. Proof: logical argument use to prove a

statement is true

7

p. 127 in your book

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download