Page 269 - Algebra 1

INVE4STIGATION
Using Deductive and Inductive Reasoning
There are two basic kinds of reasoning: deductive and inductive.
Deductive reasoning bases a conclusion on laws or rules. Inductive reasoning bases a conclusion on an observed pattern. Both types of reasoning can be used to support or justify conclusions.
All fruit have seeds. An apple is a fruit.
The two statements form an argument. The first statement is the premise, and the second statement is the conclusion. In deductive reasoning, if the argument is solid, the conclusion is guaranteed. In inductive reasoning,
if the argument is solid, the conclusion is supported but not guaranteed. Consider the following examples:
Daryl
Aliya
According to Newton’s First Law, every object will remain in uniform motion in a straight line unless compelled to change its state by the action of an external force. So, if I kick a ball, it will travel forward at a constant speed until it hits the wall.
In the past, I’ve noticed that every time I kick a soccer ball, it travels forward at a constant speed until it hits the wall. The next time I kick a ball, it will keep going until it hits the wall.
Math Language
A premise is the foundation for an argument. It is used as evidence for
the conclusion. A conclusion is an opinion or decision that logically follows the premise.
Online Connection www.SaxonMathResources.com
Daryl’s reasoning is deductive because it is based on his knowledge of Newton’s First Law of Motion. Aliya reasons inductively, basing her conclusions on her observations.
Identify the type of reasoning used. Explain your answer.
1. Premise: A student has earned a score of 100 on the last five math tests.
Conclusion: The student will earn a score of 100 on the next math test.
2. Premise: The measures of three angles of a rectangle are all 90°. Conclusion: The measure of the fourth angle is 90°.
3. Premise: A number pattern begins with 3, 5, 7, 9, 11, .... Conclusion: The next number in the pattern will be 13.
Each premise and conclusion above can be written as one sentence. For instance, the second set could be restated as, “If the measures of three angles of a rectangle are all 90°, then the measure of the fourth angle
is 90°.” This is called a conditional statement. A conditional statement is a logical statement that can be written in “if-then” form.
A conditional statement is made up of two parts: a hypothesis and a conclusion. The hypothesis is the condition. It follows the word “if.”
The conclusion is the judgment. It follows the word “then.” A conditional statement can either be true or false.
Hint
If a conditional statement is true and you apply it
to a situation in which the hypothesis is true, then you can state that the conclusion is true by deductive reasoning.
254 Saxon Algebra 1