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# Deductive logic

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• ### Transcript of "Deductive logic"

1. 1. Deductive<br />Logic<br />www.wordpandit.com<br />
2. 2. Deductive<br />Logic<br />Enter the world<br />Of Verbal Logic!<br />www.wordpandit.com<br />
3. 3. What is Deductive Logic?<br />www.wordpandit.com<br />
4. 4. What is Deductive Logic?<br />A simple combination of two words <br />www.wordpandit.com<br />
5. 5. What is Deductive Logic?<br />A simple combination of two words <br />Deductive + Logic<br />Deductive Logic<br />www.wordpandit.com<br />
6. 6. What is Deductive Logic?<br />A simple combination of two words <br />Deductive + Logic<br />Deductive Logic<br />Adjective form for deduce, <br />meaning ‘to arrive at a fact/result’<br />In layman terms, the funda/<br />reasoning behind a concept<br />www.wordpandit.com<br />
7. 7. Thus, Deductive Logic is nothing else but a method of arriving at a conclusion!<br />www.wordpandit.com<br />
8. 8. Terms in Deductive Logic<br />www.wordpandit.com<br />
9. 9. Terms in Deductive Logic<br />All men are dogs.<br />A fact/premise<br />Provided to us<br />All dogs are naughty<br />www.wordpandit.com<br />
10. 10. Terms in Deductive Logic<br />All men are dogs.<br />A fact/premise<br />Provided to us<br />The conclusion<br />We arrive at!<br />All dogs are naughty<br />Thus, all men <br />are naughty.<br />www.wordpandit.com<br />
11. 11. Guru Mantras for Deductive Logic<br />www.wordpandit.com<br />
12. 12. Guru Mantras for Deductive Logic<br />In logic, we assume <br />FACTS <br />Given to us as True!<br />www.wordpandit.com<br />
13. 13. Guru Mantras for Deductive Logic<br />In logic, we assume <br />FACTS <br />Given to us as True!<br />The result obtained<br />Should be true and….<br />www.wordpandit.com<br />
14. 14. Guru Mantras for Deductive Logic<br />In logic, we assume <br />FACTS <br />Given to us as True!<br />The result obtained<br />Should be true and….<br />And should be <br />Always true,<br />That is consistent!<br />www.wordpandit.com<br />
15. 15. Syllogisms<br />-part 1<br />Observing how words<br />Such as some, all and no<br />Function in a statement<br />www.wordpandit.com<br />
16. 16. Forms Of Premise<br />CASE 1: All A are B<br />www.wordpandit.com<br />
17. 17. Forms Of Premise<br />CASE 1: All A are B<br />A Cakewalk<br />All A are B<br />Each of A’s has to be B<br />www.wordpandit.com<br />
18. 18. Forms Of Premise<br />CASE 1: All A are B<br />A Cakewalk<br />All A are B<br />Each of A’s has to be B<br />Set representation of All A are B<br />B<br />A=B<br />A<br />www.wordpandit.com<br />
19. 19. Forms Of Premise<br />CASE 2: No A is B<br />www.wordpandit.com<br />
20. 20. Forms Of Premise<br />CASE 2: No A is B<br />Another Cakewalk<br />NO A is B<br />Not even a single can be B<br />www.wordpandit.com<br />
21. 21. Forms Of Premise<br />CASE 2: No A is B<br />Another Cakewalk<br />NO A is B<br />Not even a single can be B<br />Set representation of No A is B<br />A<br />B<br />www.wordpandit.com<br />
22. 22. Forms Of Premise<br />CASE 3: Some A are B<br />www.wordpandit.com<br />
23. 23. Forms Of Premise<br />CASE 3: Some A are B<br />‘Some’ would mean what?<br />Atleast 1 A is not B?<br />Few A are B?<br />At least 1 A is B?<br />www.wordpandit.com<br />
24. 24. Forms Of Premise<br />CASE 3: Some A are B<br />‘Some’ would mean what?<br />Atleast 1 A is not B?<br />Few A are B?<br />At least 1 A is B?<br />Means the same as<br />Some A are B<br />This would actually mean<br />‘Some A are NOT B’<br />If this is not true, then<br />No A is B<br />www.wordpandit.com<br />
25. 25. Forms Of Premise<br />CASE 3: Some A are B<br />Some A are B: Venn diagram approach<br />Set representation of Some A are B<br />Set A<br />Set B<br />www.wordpandit.com<br />
26. 26. Forms Of Premise<br />CASE 3: Some A are B<br />Some A are B: Venn diagram approach<br />Set representation of Some A are B<br />Set A<br />Set B<br />But is this ALL we can <br />do with Some A are B???<br />www.wordpandit.com<br />
27. 27. Forms Of Premise<br />CASE 3: Some A are B<br />Some A are B can be represented in the following ways:<br />Set A<br />Set B<br />www.wordpandit.com<br />
28. 28. Forms Of Premise<br />CASE 3: Some A are B<br />Some A are B can be represented in the following ways:<br />Set A=Set B<br />Set A<br />Set B<br />www.wordpandit.com<br />
29. 29. Forms Of Premise<br />CASE 3: Some A are B<br />Some A are B can be represented in the following ways:<br />Set A=Set B<br />Set A<br />Set B<br />Set B<br />Set A<br />www.wordpandit.com<br />
30. 30. Forms Of Premise<br />CASE 3: Some A are B<br />Some A are B can be represented in the following ways:<br />Set A=Set B<br />Set A<br />Set B<br />Set A<br />Set B<br />Set A<br />Set B<br />www.wordpandit.com<br />
31. 31. Forms Of Premise<br />CASE 4: Some A are not B<br />www.wordpandit.com<br />
32. 32. Forms Of Premise<br />CASE 4: Some A are not B<br />If ‘Some A are B’= ‘Atleast 1A is B’<br />then ‘Some A are not B’ simply equals to?<br />www.wordpandit.com<br />
33. 33. Forms Of Premise<br />CASE 4: Some A are not B<br />If ‘Some A are B’= ‘Atleast 1A is B’<br />then ‘Some A are not B’ simply equals to?<br />‘Atleast 1A is not B’<br />www.wordpandit.com<br />
34. 34. Forms Of Premise<br />CASE 4: Some A are not B<br />Some A are not B can be represented in the following ways:<br />Set A<br />Set B<br />www.wordpandit.com<br />
35. 35. Forms Of Premise<br />CASE 4: Some A are not B<br />Some A are not B can be represented in the following ways:<br />Set A<br />Set B<br />Set B<br />Set A<br />www.wordpandit.com<br />
36. 36. Forms Of Premise<br />CASE 4: Some A are not B<br />Some A are not B can be represented in the following ways:<br />Set A<br />Set B<br />Set B<br />Set A<br />Set B<br />Set A<br />www.wordpandit.com<br />
37. 37. Forms Of Premise<br />CASE 4: Some A are not B<br />Some A are not B can be represented in the following ways:<br />Set A=Set B<br />Set A<br />Set B<br />Set B<br />Set A<br />Set B<br />Set A<br />www.wordpandit.com<br />
38. 38. Forms Of Premise<br />CASE 4: Some A are not B<br />Some A are not B can be represented in the following ways:<br />Set A=Set B<br />Set A<br />Set B<br />Set B<br />Set A<br />Set A<br />Set B<br />Set A<br />Set B<br />www.wordpandit.com<br />
39. 39. Logical Consistency<br />-part 2<br />Introducing logic into<br />Statements with the <br />Help of conditionals such<br />As if, only and either/or!<br />www.wordpandit.com<br />
40. 40. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />www.wordpandit.com<br />
41. 41. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />www.wordpandit.com<br />
42. 42. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />1. Sachin scores a 100.<br />www.wordpandit.com<br />
43. 43. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />www.wordpandit.com<br />
44. 44. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />2. India wins the match<br />www.wordpandit.com<br />
45. 45. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />Sachin may or may not score a 100.<br />2. India wins the match<br />www.wordpandit.com<br />
46. 46. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />Sachin may or may not score a 100.<br />2. India wins the match<br />3. Sachin does not score a 100.<br />www.wordpandit.com<br />
47. 47. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />Sachin may or may not score a 100.<br />2. India wins the match<br />India may or may not win the match.<br />3. Sachin does not score a 100.<br />www.wordpandit.com<br />
48. 48. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />Sachin may or may not score a 100.<br />2. India wins the match<br />India may or may not win the match.<br />3. Sachin does not score a 100.<br />4. India does not win the match.<br />www.wordpandit.com<br />
49. 49. Case 1: If, When , Whenever<br />What happens when we use conditionals such as if, when or whenever?<br />Have a look:<br />India wins if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />Sachin may or may not score a 100.<br />2. India wins the match<br />India may or may not win the match.<br />3. Sachin does not score a 100.<br />Sachin did not score a 100.<br />4. India does not win the match.<br />The ‘If condition’ ,in other words, is a sufficient condition for the effect to happen. <br />www.wordpandit.com<br />
50. 50. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />www.wordpandit.com<br />
51. 51. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />www.wordpandit.com<br />
52. 52. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />1. Sachin scores a 100.<br />www.wordpandit.com<br />
53. 53. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />www.wordpandit.com<br />
54. 54. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />2. India wins the match<br />www.wordpandit.com<br />
55. 55. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />Sachin scores a 100.<br />2. India wins the match<br />www.wordpandit.com<br />
56. 56. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />Sachin scores a 100.<br />2. India wins the match<br />3. Sachin does not score a 100.<br />www.wordpandit.com<br />
57. 57. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />Sachin scores a 100.<br />2. India wins the match<br />India did not win the match.<br />3. Sachin does not score a 100.<br />www.wordpandit.com<br />
58. 58. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />Sachin scores a 100.<br />2. India wins the match<br />India did not win the match.<br />3. Sachin does not score a 100.<br />4. India does not win the match.<br />www.wordpandit.com<br />
59. 59. Case 2: Only If, Only When<br />What happens when we use conditionals such as only if or only when?<br />Have a look:<br />India wins only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India may or may not win the match<br />1. Sachin scores a 100.<br />Sachin scores a 100.<br />2. India wins the match<br />India did not win the match.<br />3. Sachin does not score a 100.<br />Sachin may or may not score a 100.<br />4. India does not win the match.<br />The ‘Only If condition’ ,in other words, is a necessary condition for the effect to happen. <br />www.wordpandit.com<br />
60. 60. Case 3: If & Only If, When & Only When<br />What happens when we use conditionals such as ‘if & only if’?<br />Have a look:<br />www.wordpandit.com<br />
61. 61. Case 3: If & Only If, When & Only When<br />What happens when we use conditionals such as ‘if & only if’?<br />Have a look:<br />India wins if & only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />1. Sachin scores a 100.<br />2. India wins the match<br />3. Sachin does not score a 100.<br />4. India does not win the match.<br />www.wordpandit.com<br />
62. 62. Case 3: If & Only If, When & Only When<br />What happens when we use conditionals such as ‘if & only if’?<br />Have a look:<br />India wins if & only if Sachin scores a 100.<br />Now if the conditions on the left are true, what is the outcome: <br />India wins the match<br />1. Sachin scores a 100.<br />Sachin scores a 100.<br />2. India wins the match<br />India did not win the match.<br />3. Sachin does not score a 100.<br />Sachin did not score a 100.<br />4. India does not win the match.<br />The ‘If & Only If condition’ ,in other words, is a mixture of the first two cases. <br />www.wordpandit.com<br />
63. 63. Case 4: Either A or B<br />What happens when we use conditionals such as ‘Either A or B’?<br />Have a look:<br />www.wordpandit.com<br />
64. 64. Case 4: Either A or B<br />What happens when we use conditionals such as ‘Either A or B’?<br />Have a look:<br />Either I am in eating food or watching TV.<br />Now if the conditions on the left are true, what is the outcome: <br />www.wordpandit.com<br />
65. 65. Case 4: Either A or B<br />What happens when we use conditionals such as ‘Either A or B’?<br />Have a look:<br />Either I am in eating food or watching TV.<br />Now if the conditions on the left are true, what is the outcome: <br />I am watching TV.<br />1. I am not eating food.<br />I am eating food.<br />2. I am not watching TV.<br />www.wordpandit.com<br />
66. 66. Case 4: Either A or B<br />What happens when we use conditionals such as ‘Either A or B’?<br />Have a look:<br />Either I am in eating food or watching TV.<br />Now if the conditions on the left are true, what is the outcome: <br />I am watching TV.<br />1. I am not eating food.<br />I am eating food.<br />2. I am not watching TV.<br />I may or may not be eating food.<br />3. I am watching TV.<br />I may or may not be watching TV.<br />4. I am eating food.<br />This is a tricky one. Read the notes carefully.<br />www.wordpandit.com<br />