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CS-708 1 De Morgan’s Laws – 2 - 9

De Morgan’s Laws – 2 - 9

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De Morgan’s Laws – 2 - 9. De Morgan’s Laws – 2 - 9a. Proof – 2 - 16. Proof – 2 - 16d. Application – 2 - 10. Laws of Logic – 2 - 25. Laws of Logic – 2 - 25a. Laws of Logic – 2 - 25b. Laws of Logic – 2 - 25c. Laws of Logic – 2 - 25d. Application - 1. Example - 2. Exercise – 5. - PowerPoint PPT Presentation

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Page 1: De Morgan’s Laws – 2 - 9

CS-708 1

De Morgan’s Laws – 2 - 9

Page 2: De Morgan’s Laws – 2 - 9

CS-708 2

De Morgan’s Laws – 2 - 9a

Page 3: De Morgan’s Laws – 2 - 9

CS-708 3

Proof – 2 - 16

Page 4: De Morgan’s Laws – 2 - 9

CS-708 4

Proof – 2 - 16d

Page 5: De Morgan’s Laws – 2 - 9

CS-708 5

Application – 2 - 10

Page 6: De Morgan’s Laws – 2 - 9

CS-708 6

Laws of Logic – 2 - 25

Page 7: De Morgan’s Laws – 2 - 9

CS-708 7

Laws of Logic – 2 - 25a

Page 8: De Morgan’s Laws – 2 - 9

CS-708 8

Laws of Logic – 2 - 25b

Page 9: De Morgan’s Laws – 2 - 9

CS-708 9

Laws of Logic – 2 - 25c

Page 10: De Morgan’s Laws – 2 - 9

CS-708 10

Laws of Logic – 2 - 25d

Page 11: De Morgan’s Laws – 2 - 9

CS-708 11

Application - 1

Page 12: De Morgan’s Laws – 2 - 9

CS-708 12

Example - 2

Page 13: De Morgan’s Laws – 2 - 9

CS-708 13

Exercise – 5

Page 14: De Morgan’s Laws – 2 - 9

CS-708 14

Conditional Statements - 6

Page 15: De Morgan’s Laws – 2 - 9

CS-708 15

Conditional Statements – 6a

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CS-708 16

Truth Table for p q - 8

Page 17: De Morgan’s Laws – 2 - 9

CS-708 17

Conditional Statements or Implications - 7

Page 18: De Morgan’s Laws – 2 - 9

CS-708 18

Conditional Statements OR Implications – 7a

Page 19: De Morgan’s Laws – 2 - 9

CS-708 19

Example – 9

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CS-708 20

Alternative Ways of Expressing Implications – 10

Page 21: De Morgan’s Laws – 2 - 9

CS-708 21

Alternative Ways of Expressing Implications – 10a

Page 22: De Morgan’s Laws – 2 - 9

CS-708 22

Exercise - 11

Page 23: De Morgan’s Laws – 2 - 9

CS-708 23

Exercise – 11a

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CS-708 24

Translating English Sentences to Symbols - 12

Page 25: De Morgan’s Laws – 2 - 9

CS-708 25

Translating English Sentences to Symbols – 12a

Page 26: De Morgan’s Laws – 2 - 9

CS-708 26

Translating English Sentences to Symbols – 12b

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CS-708 27

Translating English Sentences to Symbols – (3 – 12c)

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CS-708 28

Translating Symbolic Propositions to English – 13

Page 29: De Morgan’s Laws – 2 - 9

CS-708 29

Translating Symbolic Propositions to English – 13a

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CS-708 30

Translating Symbolic Propositions to English – 13b

Page 31: De Morgan’s Laws – 2 - 9

CS-708 31

Hierarchy of Operations for Logical Connectives - 14

Page 32: De Morgan’s Laws – 2 - 9

CS-708 32

Truth Table for p v ~ q ~ p – 20a

Page 33: De Morgan’s Laws – 2 - 9

CS-708 33

Truth Table for p v ~ q ~ p – 20b

Page 34: De Morgan’s Laws – 2 - 9

CS-708 34

(p q) (~p r) - 21

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CS-708 35

(p q) (~p r) – 21a

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CS-708 36

(p q) (~p r) – 21c

Page 37: De Morgan’s Laws – 2 - 9
Page 38: De Morgan’s Laws – 2 - 9

CS-708 38

p q ≡ ~q ~p- 22

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CS-708 39

Implication Law – 23

Page 40: De Morgan’s Laws – 2 - 9

CS-708 40

Negation of a Conditional Statement - 15

Page 41: De Morgan’s Laws – 2 - 9

CS-708 41

Examples – (3 - 16)

Page 42: De Morgan’s Laws – 2 - 9

CS-708 42

Example – 16a

Page 43: De Morgan’s Laws – 2 - 9

CS-708 43

Inverse of a Conditional Statement - 24

Page 44: De Morgan’s Laws – 2 - 9

CS-708 44

p q is not equivalent to ~p ~q – (3 – 25)

Page 45: De Morgan’s Laws – 2 - 9

CS-708 45

Writing Inverse – 17

Page 46: De Morgan’s Laws – 2 - 9

CS-708 46

Writing Inverse – 17a

Page 47: De Morgan’s Laws – 2 - 9

CS-708 47

Converse of a Conditional Statement - 26

Page 48: De Morgan’s Laws – 2 - 9

CS-708 48

Converse of a conditional Statement – (3 – 27)

Page 49: De Morgan’s Laws – 2 - 9

CS-708 49

Writing Converse – 18

Page 50: De Morgan’s Laws – 2 - 9

CS-708 50

Writing Converse – 18a

Page 51: De Morgan’s Laws – 2 - 9

CS-708 51

Contrapositive of a Conditional Statement– 28

Page 52: De Morgan’s Laws – 2 - 9

CS-708 52

Writing Contrapositivity – 19

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CS-708 53

Writing Contrapositivity – 19a

Page 54: De Morgan’s Laws – 2 - 9

CS-708 54

Biconditional - 2

Page 55: De Morgan’s Laws – 2 - 9

CS-708 55

Truth Table for p <--> - 3

Page 56: De Morgan’s Laws – 2 - 9

CS-708 56

Examples – 4a

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CS-708 57

Examples – 4b

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CS-708 58

p q = (p q) (q p) – 5av

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CS-708 59

p q = (p q) (q p) – 5bv

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CS-708 60

p q = (p q) (q p) – 5cv

– 5c

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CS-708 61

vp q = (p q) (q p) – 5

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CS-708 62

Rephrasing Biconditional - 6

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CS-708 63

Examples – 9

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CS-708 64

Examples – 9a

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CS-708 65

Examples – 9b

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CS-708 66

Examples – 9c

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CS-708 67

Truth table for (p q) (~q ~p) – 7a

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CS-708 68

Truth table for (p q) (~q ~p) – 7b

Page 69: De Morgan’s Laws – 2 - 9

CS-708 69

Truth table for (p q) (~q ~p) – 7c

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CS-708 70

Truth table for (p q) (~q ~p) – 7

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CS-708 72

(p q) (r q) – 8

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CS-708 73

(p q) (r q) – 8b

Page 74: De Morgan’s Laws – 2 - 9

CS-708 74

(p q) (r q) – 8c

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CS-708 75

(p q) (r q) – 8d

Page 76: De Morgan’s Laws – 2 - 9

CS-708 76

(p q) (r q) – 8

Page 77: De Morgan’s Laws – 2 - 9

CS-708 77

p ~ r q v r – 10v

Page 78: De Morgan’s Laws – 2 - 9

CS-708 78

p ~ r q v r – 10bv

Page 79: De Morgan’s Laws – 2 - 9

CS-708 79

p ~ r q v r – 10cv

Page 80: De Morgan’s Laws – 2 - 9

CS-708 80

p ~ r q v r – 10dv

Page 81: De Morgan’s Laws – 2 - 9

CS-708 81

p ~ r q v r – 10ev

Page 82: De Morgan’s Laws – 2 - 9

CS-708 82

Show that ~p q ≡ p ~q – 11a

Page 83: De Morgan’s Laws – 2 - 9

CS-708 83

Show that ~p q ≡ p ~q – 11b

Page 84: De Morgan’s Laws – 2 - 9

CS-708 84

Show that ~p q ≡ p ~q – 11

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CS-708 85

Show that ~p q ≡ p ~q – 11c

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CS-708 86

Show that ~(p + q) ≡ p q – 12b

Page 87: De Morgan’s Laws – 2 - 9

CS-708 87

Show That - 1(4 - 2c)

Page 88: De Morgan’s Laws – 2 - 9

CS-708 88

Show that ~(p + q) ≡ p q – 12d

Page 89: De Morgan’s Laws – 2 - 9

CS-708 89

Show that ~(p + q) ≡ p q – 12

Page 90: De Morgan’s Laws – 2 - 9

CS-708 90

Laws of Logic – 14

Page 91: De Morgan’s Laws – 2 - 9

CS-708 91

Laws of Logic - 14a

Page 92: De Morgan’s Laws – 2 - 9

CS-708 92

Application – 15

Page 93: De Morgan’s Laws – 2 - 9

CS-708 93

Application – 15b

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CS-708 94

Exercise - 17

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CS-708 95

Exercise – 17a

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CS-708 96

Exercise – 17b