SECTION 2.3

DED

UCTIVE R

EASO

NIN

G

INDUCTIVE VS. DEDUCTIVEREASONING

Do you remember what Inductive Reasoning is?

Reasoning based on patterns you observe

Deductive Reasoning (logical reasoning)

Process of reasoning logically from given statements to a

conclusion.

In other words…

INDUCTIVE REASONING uses rules to make conclusions

DEDUCTIVE REASONING uses examples to make conclusions

LAW OF DETACHMENT

If a conditional is true and its hypothesis is true, then its conclusion

is true.

In Symbolic Form:

If p q is a true statement and p is true, then q is true.

Example 1: Using the Law of Detachment

If an angle is obtuse, then it cannot be acute.

Angle B is obtuse.

CONCLUSION: Angle B cannot be acute

LAW OF DETACHMENT CONT…

Example 2: Using the Law of Detachment

If Z is the midpoint of a segment, then it divides the segment into

two congruent segments.

Z is the midpoint of ST

CONCLUSION: Z divides ST into two congruent segments.

Example 3: Using the Law of Detachment

If a road is icy, then driving conditions are hazardous.

Driving conditions are hazardous.

CONCLUSION: Not possible; you do not know the hypothesis is true

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.

NOTE: This is like the Transitive Property

If a = b and b = c, then a = c

In Symbolic Form:

If p q and q r are true statements, then p r is a true statement

Example 1: Using the Law of Syllogism

If it is Sunday, the Mr. Z has a lot of free time.

If Mr. Z has a lot of free time, then he will watch football

CONCLUSION: If it is Sunday, the Mr. Z will watch football

LAW OF SYLLOGISM CONT…

Example 2:

If it is 7:30 AM, then the Libertyville high school day begins.

If the Libertyville high school day begins, then Jason will report to his 1st hour

class.

CONCLUSION: If it is 7:30 AM, then Jason will report to his 1st hour class.

Example 3:

If two angles are a linear pair, then their sum is 180 degrees.

If two angles are a linear pair, then they are adjacent angles.

CONCLUSION: Not Possible; q r