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COMP 170 L2 L08: Quantifiers. COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified.

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Presentation on theme: "COMP 170 L2 L08: Quantifiers. COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified."— Presentation transcript:

1 COMP 170 L2 L08: Quantifiers

2 COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified Statements l Proving Quantified Statements True or False l Quantifiers and Negation Page 2

3 COMP 170 L2 Quantifiers: Motivation Page 3

4 COMP 170 L2 Quantifiers: Motivation Page 4

5 COMP 170 L2 Quantifiers Page 5

6 COMP 170 L2 Universal Quantifier Page 6

7 COMP 170 L2 Universal Quantifier Page 7

8 COMP 170 L2 Existential Quantifier Page 8

9 COMP 170 L2 Proving Quantified Statements Page 9

10 COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified Statements l Proving Quantified Statements True or False l Quantifiers and Negation Page 10

11 COMP 170 L2 Standard Notation of Quantification Page 11

12 COMP 170 L2 Meaning of Quantified Statements Page 12

13 COMP 170 L2 Meaning of Quantified Statements Page 13

14 COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified Statements l Proving Quantified Statements True or False l Quantifiers and Negation Page 14

15 COMP 170 L2 Saying Things using Quantified Statements Page 15

16 COMP 170 L2 Saying Things using Quantified Statements Page 16

17 COMP 170 L2 Change Universes in Quantified Statements Page 17

18 COMP 170 L2 Page 18

19 COMP 170 L2 Change Universes in Quantified Statements Page 19

20 COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified Statements l Proving Quantified Statements True or False l Quantifiers and Negation Page 20

21 COMP 170 L2 Proving Quantified Statements True or False Page 21

22 COMP 170 L2 Proving Quantified Statements True or False Page 22

23 COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified Statements l Proving Quantified Statements True or False l Quantifiers and Negation Page 23

24 COMP 170 L2 Page 24

25 COMP 170 L2 Negation and Universal Quantifier Page 25

26 COMP 170 L2 Page 26

27 COMP 170 L2 Page 27

28 COMP 170 L2 Page 28

29 COMP 170 L2 Final Note l Implicit quantification in natural language Page 29

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