Bell WorkIf x=4, then
Write the hypothesis
Write the Conclusion
Write the converse
What is the Biconditional?
Chapter 2.3 Deductive Reasoning1.0 Students demonstrate understanding by identifying and giving examples of deductive reasoning
VocabularyDeductive Reasoning (logical reasoning) = the process of reasoning logically from given statements to a conclusion. You conclude from facts.
Example A physician diagnosing a patients illness uses deductive reasoning. They gather the facts before conclusion what illness it is
Whats the difference between inductive and deductive reasoning?
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
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
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
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!!!
Quick SummaryYou can only conclude if you are given the hypothesis!!!
If you are given the conclusion you CAN NOT prove the hypothesis
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.
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
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
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?
HomeworkP 96 #2, 4, 8, 10, 11, 12, 14