Section 2.3 – Deductive Reasoning Continued
*Watch this video to give you a better grasp of the concepts listed below.*
Deductive Reasoning: Uses facts, definitions, and accepted properties in a logical order to write a logical
argument.
Inductive Reasoning: Uses previous examples and patterns to form a conjecture.
Example 1: Is the reasoning inductive or deductive?
a) Josh knows that Brand X computers cost less than Brand Y computers. All other brands that Josh
knows of cost less than Brand X. Josh reasons that Brand Y costs more than all other brands.
b) Josh knows that Brand X computers cost less than Brand Y computers. He also knows that Brand Y
computers cost less than Brand Z. Josh reasons that Brand X costs less than Brand Z.
Two laws of deductive reasoning:
1. Law of Detachment
If p
q is a true conditional statement and p is true, then q is true.
2. Law of Syllogism
If p
q and q
r are true conditional statements, then p
r is true.
Example 2: State whether the argument is valid.
a) Sarah knows that all sophomores take driver education in her school. Hank is a sophomore at Sarah's
school. So Hank takes driver education.
b) If two angles form a linear pair, then they are supplementary; A and B are supplementary. So A
and B form a linear pair.
Example 3: State whether any conclusions can be made using the true statement, given that
a) If
, then
.
b) If
0, then
.
.
Example 4: Write some conditional statements that can be made from the following true statements
using the Law of Syllogism.
1.
2.
3.
4.
If it is lightening outside, then the football game will get cancelled.
If the football game gets cancelled, then the players will not be on the field.
If the players are not on the field, then the coaches will not be on the field.
If the coaches are not on the field, then the team cannot practice.
Example 5: Write some conditional statements that can be made from the following true statements
using the Law of Syllogism.
1.
2.
3.
4.
5.
If a fish swims at 68 mph, then it swims at 110 km/h.
If a fish can swim at 110 km/h, then it is a sailfish.
If a fish is the largest species of fish, then it is a great white shark.
If a fish weighs over 200 lbs, then it is the largest species of fish.
If a fish is the fastest species of fish, then it can reach speeds of 68 mph.
Example 6: Use the diagram to give a reason for each true statement. m 2=107, 6
a) m 2 = 107
b) If m 2=107, then m 6=73.
c) If m 6=73, then m 4=73.
d) If m 4=73, then m 3=73.
e) If m 3=73, then m 5=73.
f) If m 5=73, then m 1=107.
g) If m 2=107, then m 1=107.
*Watch this video to see the examples worked through*
4, 3
5