Is there any proof that the Bible is true?

2. Is there any proof that the Bible is true?

3. TYPES OF REASONING Inductive Versus Deductive Reasoning

4. Inductive Versus Deductive Reasoning • There are two approaches to furthering knowledge • reasoning from known ideas and • synthesize observations.

5. Inductive Versus Deductive Reasoning In inductive reasoning you observe the world, and attempt to explain based on your observations. You start with no prior assumptions. Deductive reasoning consists of logical assertions from known facts.

7. INDUCTIVE REASONING • reaching a conclusion based on previous observation. • It moves from the specific to the general Types of reasoning

8. EXAMPLES 1² = 1 1 ≤ 1 2² = 4 2 ≤ 4 3² = 9 3 ≤ 9 (-1)² = 1 -1 ≤ 1 BASED ON THE GIVEN EXAMPLES, DRAW A CONCLUSION/S.

9. BASED ON THE EXAMPLES, WE NOTICED A PATTERN FROM WHICH WE DRAW A CONCLUSIONS. Examples 1² = 1 1 ≤ 1 2² = 4 2 ≤ 4 3² = 9 3 ≤ 9 (-1)² = 1 -1 ≤ 1 Types of reasoning

10. THROUGH INDUCTIVE REASONING, IT MAY BE CONCLUDED THAT WHENEVER A NUMBER IS SQUARED, THE RESULT IS A NUMBER WHICH IS GREATER THAN OR EQUAL TO THE ORIGINAL NUMBER. Examples 1² = 1 1 ≤ 1 2² = 4 2 ≤ 4 3² = 9 3 ≤ 9 (-1)² = 1 -1 ≤ 1 Types of reasoning

11. Inductive reasoning is making conclusions based on patterns you observe.The conclusion you reach is called a conjecture Examples 1² = 1 1 ≤ 1 2² = 4 2 ≤ 4 3² = 9 3 ≤ 9 (-1)² = 1 -1 ≤ 1 Types of reasoning

12. INDUCTIVE REASONING • reaching a conclusion based on previous observation. • b. Conclusions are probably TRUE but not necessarily TRUE. Types of reasoning

13. Conclusion: 2² = 4 2 ≤ 4 3² = 9 3 ≤ 9 (-1)² = 1 -1 ≤ 1 Consider this example (½) ²= ¼ ½> ¼ Does the conclusion hold true? “WHENEVER A NUMBER IS SQUARED, THE RESULT IS A NUMBER WHICH IS GREATER THAN OR EQUAL TO THE ORIGINAL NUMBER.” No. Because ½ is greater than ¼. Types of reasoning

14. INDUCTIVE REASONING • reaching a conclusion based on previous observation. • b. Conclusions are probably TRUE but not necessarily TRUE. Types of reasoning

15. Another example A BEGINNING OBSERVER OF AMERICAN BASEBALL MAY CONCLUDE, AFTER WATCHING SEVERAL GAMES, THAT THE GAME IS OVER AFTER 9 INNINGS. HE WILL ONLY REALIZE THAT THIS OBSERVATION IS FALSE AFTER OBSERVING A GAME WHICH IS TIED AFTER 9 INNINGS.

16. INDUCTIVE REASONNG INDUCTIVE REASONING IS USEFUL BUT NOT CERTAIN.THERE WILL ALWAYS BE A CHANCE THAT THERE IS AN OBSERVATION THAT WILL SHOW THE REASONING TO BE FALSE. ONLY ONE OBSERVATION IS NEEDED TO PROVE THE CONCLUSION TO BE FALSE. Types of reasoning

17. Try this.

18. Look carefully at the following figures. Then, use inductive reasoning to make a conjecture about the next figure in the pattern If you have carefully observed the pattern, may be you came up with the figure below: Types of reasoning

19. Look at the patterns below. Can you draw the next figure or next set of dots using inductive reasoning? The trick is to see that one dot is always placed between and above two dots. Also, the next figure always has one more dot at the very bottom rowkeeping this in mind, your next figure should look like this: Types of reasoning

20. Inductive reasoning is used often in life. Polling is an example of the use of inductive reasoning. If one were to poll one thousand people, and 300 of those people selected choice A, then one would infer that 30% of any population might also select choice A. This would be using inductive logic, because it does not definitively prove that 30% of any population would select choice A. Types of reasoning

21. DEDUCTIVE REASONNG • reaching a conclusion by combining known truths to create a new truth • b. deductive reasoning is certain, provided that the previously known truths are in fact true themselves. Types of reasoning

22. Examples 1. An angle is congruent to itself. 2. Mr. Samuel M. Gier is a math teacher. 3. If 2x = 8, then x = 4. Types of reasoning

23. FORMS OF DEDUCTIVE REASONNG There are a few forms of deductive logic. One of the most common deductive logical arguments is modus ponens, which states that: p ⇒ q read as “If p, then q”. p ∴ q read as “p, therefore q” Types of reasoning

24. Example of modus ponens If I stub my toe, then I will be in pain. I stub my toe. Therefore, I am in pain. Types of reasoning

25. FORMS OF DEDUCTIVE REASONNG Another form of deductive logic is modus tollens, which states the following. p ⇒ q read as “If p, then q”. ¬q ∴ ¬p read as “not q, therefore not p” Types of reasoning

26. Example of modus tollens If today is Thursday, then the cafeteria will be serving burritos. The cafeteria is not serving burritos, therefore today is not Thursday. Types of reasoning

27. FORMS OF DEDUCTIVE REASONNG Another form of deductive logic is known as the If-Then Transitive Property. Simply put, it means that there can be chains of logic where one thing implies another thing. The If-Then Transitive Property states: p ⇒ q read as “If p, then q”. (q ⇒ r) ∴ (p ⇒ r) read as ((If q, then r), therefore (if p, then r)) Types of reasoning

28. Example of If-Then Transitive Property If today is Thursday, then the cafeteria will be serving burritos. If the cafeteria will be serving burritos, then I will be happy. Therefore, if today is Thursday, then I will be happy. Types of reasoning

29. DEDUCTIVE REASONNG Deductive reasoning is based on laws or general principles. People using deductive reasoning apply a general principle to a specific example. Types of reasoning

30. Choosing a Strategy Use inductive reasoning to form arguments based on experience. Use deductive reasoning to form arguments based on rules or previously known facts. Types of reasoning

31. How much do you know Answer orally

32. EXERCISES All vegetables are good for you. Broccoli is a vegetable. Therefore, broccoli is good for you. This is an example of what type of reasoning? DEDUCTIVE REASONING Types of reasoning

33. EXERCISES Broccoli is a vegetable. Broccoli is a green. Therefore, all vegetables are green. Why is this conclusion invalid? Types of reasoning

34. What is a proof? This is a form of logical reasoning from hypothesis to conclusion. In geometry it is defined as “a method of constructing a valid argument”. According to Thesaurus (synonyms) Evidence Testimony Verification Confirmation Subtantiation PROOF

35. An INDIRECT PROOF or proving by contradiction is a proof written in paragraph form. Indirect proof And Direct proof KINDS OF PROOF

36. HOMEWORK • Give two examples using deductive and inductive reasoning. Write your answers in a paper (one-half crosswise)