Inductive- Reasoning - MMW PDF

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CHAPTER 3: PROBLEM-SOLVING AND REASONING

INDUCTIVE REASONING Sir Francis Bacon -

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He works mainly on the possibility of scientific knowledge based only upon inductive reasoning and careful observation of events in nature. One of the founders of Modern Science

Modern Science 

the first formulation of Modern Scientific Method.

the

Baconian Method  

the investigative method developed by Sir Francis Bacon. an example of the application of Inductive Reasoning

To understand inductive reasoning clearly. Consider the following story.

Someone brought a basket of tomatoes to Alvin’s house. “Alvin, look at the tomatoes in the basket and check if they are RIPE or RAW,” mother said.  Alvin took a tomato. It is RED, so it is ripe .  He took another tomato. It is also RED, so it is ripe.  Alvin took a tomato for the third time. It is still RED, so it is ripe . “Ma, all the tomatoes are ripe,” Alvin concluded.

Inductive Reasoning 

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the process of reaching a general conclusion by examining specific example Specific  General based on the examination of specific examples that forms a general conclusions. SPECIFIC EXAMPLES

Alvin concluded that all tomatoes are ripe. He used inductive reasoning. Because he made a general conclusion out of specific examples.

Do you think it is correct? Let’s continue the story and see how Alvin’s conjecture MAY or MAY NOT be correct. “Take a good look,” mother said.

GENERAL CONCLUSION

The conclusion is called CONJECTURE, may or may not be correct.

“Mom, look at everything, they are all ripe.” Alvin replied.

CHAPTER 3: PROBLEM-SOLVING AND REASONING Thus, Alvin’s CORRECT

CONJECTURE

is

What if we change the ending?

Practice Exercise:

But the mother did not believe. She looked at all tomatoes. She was surprised by what she saw. She asked Alvin, “Are these ripe my son?” And Alvin looked with astonishment.

Alvin’s Hence, INCORRECT.

CONJECTURE

is

Let us relate inductive reasoning to our present situation. Let’s talk about vaccine.  Statement 1: The COVID-19 Vaccine developed by  PHARMA PASSED the phase 1 of Clinical trial.  Statement 2: The COVID-19 Vaccine developed by  PHARMA PASSED the phase 2 of Clinical trial.  Statement 3: The COVID-19 Vaccine developed by  PHARMA PASSED the phase 3 of Clinical trial.

Conclusion: The COVID-19 Vaccine developed by  PHARMA is effective and safe.

Determine whether the argument is an example of inductive reasoning or not.

1. The Los Angeles Lakers have won four games to dispatch the Portland Trailblazers. Therefore, the Los Angeles Lakers will win their next game. Answer: Inductive Reasoning

2. All quadrilaterals have exactly four sides. Rectangle is a quadrilateral. therefore, rectangle has exactly four sides. Answer: Not inductive reasoning

3. Alvin enjoyed Ligaya, Pare Eraserheads. listening to Eraserheads.

listening to the song Ko, and Toyang by So, he will enjoy the next song of

Answer: Inductive Reasoning

CHAPTER 3: PROBLEM-SOLVING AND REASONING Leo Moser  Lesson 2: Number Patterns Isaiah Berlin To understand patterns.

is

to

perceive

Pick a number, multiply the original number by 6. Add 8 to the product. Divide the sum by 2. Subtract 4.

Lesson 3: Letter Patterns Dennis Prager Finding patterns is the essence of Wisdom.

Lesson 4: Ab stract Reasoning Alfred North Whitehead The certainty of mathematics depends on its complete abstract generality.

The enumeration of the regions formed when circle is divided by secants drawn from points on the circle is one of the examples where the inductive reasoning fails as pointed.

Moser’s Circle Problem The problem of dividing a circle into areas by means of n points on a circle in such a way as to maximize the number of areas or regions created by the edges and diagonals connecting the points is called Moser’s Circle Problem.

Remember: If a pattern holds true for a few cases, it does not mean the pattern will continue. If you use inductive reasoning, you have no guarantee that your conclusion is correct. We can disprove the answer of inductive reasoning by giving counterexample.

Abstract Reasoning 

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also known as conceptual reasoning are non-verbal in nature and consist of questions including shapes and images. measures lateral thinking and fluid intelligence with the sole purpose of determining how quickly you can identify patterns, logical rules and data trends.

Lesson 6: Moser’s Circle Problem

Lesson 7: Counterxample Aristotle He proves invalidity by constructing counterexample. Definition: is an example that opposes or contradicts an idea or theory.

CHAPTER 3: PROBLEM-SOLVING AND REASONING  

Lesson 8: DEDUCTIVE Rene Descartes

REASONING

His book Discourse on Method (1637) describes how scientific study should be prosecuted so as to achieve the utmost clarity, by using deductive reasoning to test hypothesis.

 

Types of KenKen Puzzles 

Deductive Reasoning 

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the process of reaching a specific conclusion by applying general assumptions General  specific

Tetsuya Miyamoto trademarked name for an arithmetic-based logic puzzle invented in 2004 by a Japanese math teacher. The noun ken is synonymous to ‘knowledge’ or ‘awareness’ KenKen  “knowledge squared”, “awareness squared”

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ranges from 3x3 to 9x9. -6x6 Parts of a KenKen Puzzle composed of heavily outlined sets of squares. Each set of heavily outlined squares is called CAGE.

Cage General Assumptions, Procedures or Principles (down arrow) General Conclusion

Lesson 10: Logic Puzzle

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Rules for Solving a KenKen Puzzle   

Logic Puzzle 

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introduced by Charles Lutwidge Dodgson. His pen name is Lewis Carroll, the author of Alice Adventure in Wonderland. can be solved by chart that enables us to display the given information in a visual manner.

FRACTIONS are NOT ALLOWED DECIMALS are NOT ALLOWED NON-POSITIVE INTEGERS are NOT ALLOWED

Lesson 12: Magic Square Magic Square -

Lesson 11: Kenken Puzzle KenKen

has a number and an operation in the top left corner.

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The best-known early square is probably the 4x4 magic square depicted in 1514 in Albrecht Durer’s woodcut “Melancholia” kind of recreational mathematics and combinatorial design. is a nxn square grid (where n is the number of squares on each side).

CHAPTER 3: PROBLEM-SOLVING AND REASONING

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the 1x1 magic square, with only one cell containing the number 1 is called trivial. Normal magic squares of all sizes can be constructed except 2x2. filled with distinct positive integers in the range 1,2,3, …, n2.

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If it is a 3x3 square grid, the cells are filled with the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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If it is a 4x4 square grid, the cells are filled with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16. If it is a 5x5 square grid, the cells are filled with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, and 25.

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