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Bell WorkIf x=4, then
Write the hypothesis
Write the Conclusion
Write the converse
What is the Biconditional?
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Chapter 2.3 Deductive Reasoning1.0 Students demonstrate
understanding by identifying and giving examples of deductive
reasoning
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VocabularyDeductive Reasoning (logical reasoning) = the process
of reasoning logically from given statements to a conclusion. You
conclude from facts.
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Example A physician diagnosing a patients illness uses deductive
reasoning. They gather the facts before conclusion what illness it
is
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Whats the difference between inductive and deductive
reasoning?
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Law of DetachmentLaw 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
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Law of Detachment ExampleUse Law of Detachment to draw a
conclusion
If a student gets an A on a final exam, then the student will
pass the course.
Felicia gets an A on the music theory final exam
Conclusion: She will pass Music Theory class
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Law of Detachment: Try itUse Law of Detachment to draw a
conclusion
If its snowing, then the temperature is below 0 degrees
It is snowing outside
Conclusion: Its below 0 degrees
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Law of Detachment Example: Careful!
Use the Law of Detachment to draw a conclusionIf a road is icy,
then driving conditions are hazardous
Driving conditions are hazardous
Conclusion: You cant conclude anything!!!
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Quick SummaryYou can only conclude if you are given the
hypothesis!!!
If you are given the conclusion you CAN NOT prove the
hypothesis
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Law of SyllogismIf pq and qr are true statements, the pr is a
true statement
Example:
If the electric power is cut, then the refrigerator does not
work.
If the refrigerator does not work, then the food is spoiled. So
if the electric power is cut, then the food is spoiled.
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Law of Syllogism example:Use law of syllogism to draw a
conclusion
If you are studying botany, then you are studying biology.If you
are studying biology, then you are studying a science
Conclusion: If you are studying botany, then you are studying a
science
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Law of Syllogism: Try itUse the law of Syllogism and draw a
conclusion
If you play video games, then you dont do your homework
If you dont do your homework, then your grade will drop
Conclusion: If you play video games, then your grade will
drop
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Activity (5 min)Write the summary about this section in your
Cornell note.
Some questions to consider:What is the topic about?What did I
learn from this lesson?What questions do I have?How does it relate
to other lessons/real life?
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HomeworkP 96 #2, 4, 8, 10, 11, 12, 14
