Over the years you have made conjectures, using inductive reasoning, based on patterns you have...
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Transcript of Over the years you have made conjectures, using inductive reasoning, based on patterns you have...
![Page 1: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/1.jpg)
Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed.
When you make a conjecture, the process of discovery may not always help explain why the conjecture works.
You need another kind of reasoning to help answer this question.
![Page 2: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/2.jpg)
Deductive Reasoning is the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts. When you use deductive reasoning, you try to
reason in an orderly way to convince others that your conclusion is valid.
Examples: Lawyers use deductive arguments to prove their case to a jury. Every time you show your work in a math problem you are using deductive reasoning…. Let’s see an example…
![Page 3: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/3.jpg)
3(2x+1) + 2(2x+1) + 7 = 42 – 5x 5(2x+1) + 7 = 42 – 5x 5(2x+1) = 35 – 5x 10x + 5 = 35 – 5x 10x = 30 – 5x 15x = 30 x = 2
This is the work you
are used to showing
when solving
algebraic equations.
![Page 4: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/4.jpg)
3(2x+1) + 2(2x+1) + 7 = 42 – 5x
Original Equation
5(2x+1) + 7 = 42 – 5x
Combining Like Terms
5(2x+1) = 35 – 5x
Subtraction Property of Equality
10x + 5 = 35 – 5x
Distributive Property
10x = 30 – 5x
Subtraction Property of Equality
15x = 30
Addition Property of Equality
x = 2
Division Property of Equality
Here we have given specific reasons for each step and have formed a logical
argument that x=2.
*This is deductive reasoning.*
![Page 5: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/5.jpg)
If Manuel has a healthy diet, then he will have a healthy body.
If Manuel has a healthy body, then he will feel good.
Syllogism: If Manuel has a healthy diet, then he will feel good.
![Page 6: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/6.jpg)
If the season is Fall, then the leaves will change colors.
If the leaves change colors, then they will fall from the trees.
Syllogism: If the season is Fall, then the leaves will fall from the trees!
![Page 7: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/7.jpg)
If you are at least 16 years old, you can get a drivers license.
Ricky is 16 years old.
Detachment: Ricky can get a drivers license.
![Page 8: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/8.jpg)
If 2x > 10, then 2x > 7. If x > 5, then 2x > 10. Syllogism: If x > 5, then 2x > 7.
![Page 9: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/9.jpg)
If you study hard, you will pass all of your classes. If you pass all of your classes, you will graduate.
Syllogism: If you study hard, then you will graduate.
![Page 10: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/10.jpg)
If x2 > 9, then x2 > 8. If x > 4, then x2 > 9.
Syllogism: If x > 4 , then x2 > 8.
![Page 11: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/11.jpg)
If you like pizza, you love Chicago style deep dish. Emily loves Chicago style deep dish.
Detachment: Emily loves pizza.
![Page 12: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/12.jpg)
If Ron eats lunch today, then he will eat a sandwich. If Ron eats a sandwich, then he will drink a glass of milk.
Syllogism: If Ron eats lunch today, then he will drink a glass of milk.
![Page 13: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/13.jpg)
If you want an “A” in Geometry, you will have to study hard. Sal is studying hard.
Detachment: Sal will get an “A” in Geometry.
![Page 14: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/14.jpg)
If you do your homework, then you can watch TV. If you watch TV, then you can watch your favorite show
Syllogism: If you do your homework, then you can watch your favorite TV show.
![Page 15: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/15.jpg)
If Kendra pops a bag of popcorn, then she will eat the popcorn. If Kendra eats the popcorn, then she will need something to drink.
Syllogism: If Kendra pops a bag of popcorn, then she will need something to drink.
![Page 16: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/16.jpg)
If you give Kfed money, then he makes an awesome album.
Hypothesis- Conclusion-
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The ______ of a conditional statement is formed by exchanging the hypothesis and the conclusion.
Conditional- If it is sunny outside, then it is hot.
Converse- If it is hot, then it is sunny outside.
![Page 18: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/18.jpg)
What are the key words included in a biconditional statement?
![Page 19: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/19.jpg)
What is the inverse of the following statement.
Example:
Cond. Stmt: If is sunny outside, then it is hot.
Inverse: If it is NOT sunny outside, then it is NOT hot.
![Page 20: Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of.](https://reader035.fdocuments.us/reader035/viewer/2022062802/56649ee55503460f94bf3dec/html5/thumbnails/20.jpg)
Example:
Cond. Stmt: If it is sunny outside, then it is hot.
Converse: If it is hot, then it is sunny outside.
Contrapositive:If it is NOT hot, then it is NOT sunny.
What is the contrapositive for the following statement?
If it is sunny outside, then it is hot.