Download Deductive Reasoning 2

Deductive Reasoning
LESSON 2-3
Additional Examples
A gardener knows that if it rains, the garden will be
watered. It is raining. What conclusion can he make?
The first sentence contains a conditional statement. The hypothesis is
“It rains.”
Because the hypothesis is true, the gardener can conclude that the
garden will be watered.
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HELP
GEOMETRY
Deductive Reasoning
LESSON 2-3
Additional Examples
For the given statements, what can you conclude?
Given: If A is acute, mA < 90.
A is acute.
A conditional and its hypothesis are both given as true.
By the Law of Detachment, you can conclude that the conclusion of
the conditional mA < 90 is also true.
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GEOMETRY
Deductive Reasoning
LESSON 2-3
Additional Examples
Does the following argument illustrate the Law of
Detachment?
Given: If you make a field goal in basketball, you score two points.
Jenna scored two points in basketball.
You conclude: Jenna made a field goal.
The two given statements mean that a conditional and its conclusion
are both true.
The Law of Detachment applies only if a conditional and its hypothesis
are true.
You can make no conclusion. You cannot conclude that Jenna made a
field goal.
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GEOMETRY
Deductive Reasoning
LESSON 2-3
Additional Examples
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.
The conclusion of the first conditional is the hypothesis of the second
conditional. This means that you can apply the Law of Syllogism.
The Law of Syllogism: If p  q and q  r are true, then p  r is a true
statement.
So you can conclude: If a quadrilateral is a square, then it is a
rectangle.
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GEOMETRY
Deductive Reasoning
LESSON 2-3
Additional Examples
Use the Laws of Detachment and Syllogism to
draw a possible conclusion.
If the circus is in town, then there are tents at the fairground.
If there are tents at the fairground, then Paul is working as a night
watchman.
The circus is in town.
Because the conclusion of the first statement is the hypothesis of the
second statement, you can apply the Law of Syllogism to write this
new conditional:
If the circus is in town, then Paul is working as a night watchman.
The third statement means that the hypothesis of the new conditional
is true. You can use the Law of Detachment to form the conclusion:
Quick Check
Paul is working as a night watchman.
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GEOMETRY