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12.2: And and Or in Logic 1/17/2014 12.2: And, Or and Not in Logic Expectations: L3.2.1:Know and use the terms of basic logic (e.g., proposition, negation,

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Presentation on theme: "12.2: And and Or in Logic 1/17/2014 12.2: And, Or and Not in Logic Expectations: L3.2.1:Know and use the terms of basic logic (e.g., proposition, negation,"— Presentation transcript:

1 12.2: And and Or in Logic 1/17/ : And, Or and Not in Logic Expectations: L3.2.1:Know and use the terms of basic logic (e.g., proposition, negation, truth and falsity, implication, if and only if, contrapositive, and converse). L3.2.2:Use the connectives not, and, or, and if..., then, in mathematical and everyday settings. Know the truth table of each connective and how to logically negate statements involving these connectives. L3.2.3:Use the quantifiers there exists and all in mathematical and everyday settings and know how to logically negate statements involving them.

2 12.2: And and Or in Logic 1/17/2014 Statements Statement in Logic: Sentence that is either true or false. Compound Statement: 2 or more statements connected together usually by and or or.

3 12.2: And and Or in Logic 1/17/2014 Conjunction: Compound statement using _____ as the connector. p ____ q

4 12.2: And and Or in Logic 1/17/2014 Ex: A square is a rhombus and it is a rectangle. p: a square is a rhombus q: a square is a rectangle

5 12.2: And and Or in Logic 1/17/2014 A conjunction is true iff p and q are ___________.

6 12.2: And and Or in Logic 1/17/2014 Truth table for conjunctions. pqtrue truefalse falsetruefalse p and q

7 12.2: And and Or in Logic 1/17/2014 Is the following conjunction true or false? Parallel lines do not intersect and perpendicular lines do intersect.

8 12.2: And and Or in Logic 1/17/2014 Disjunction: Compound statement using ____ as the connector. p ____ q

9 12.2: And and Or in Logic 1/17/2014 Exclusive or: one or the other but not both. Betty is right handed or she is left handed. Inclusive or: one or the other or both. It may be cloudy or cool tomorrow.

10 12.2: And and Or in Logic 1/17/2014 Disjunctions use the ________ or.

11 12.2: And and Or in Logic 1/17/2014 Truth table for disjunctions. pqtrue truefalse falsetruefalse p or q

12 12.2: And and Or in Logic 1/17/2014 Is the following disjunction true or false? A rectangle has at least 2 right angles or a square is a closed 3 sided figure.

13 12.2: And and Or in Logic 1/17/2014 Quantifiers Three common geometric quantifiers are there exists, all and every. There exists just means ______________ of something exists. All and every basically mean the same thing: each and every thing must satisfy the condition.

14 12.2: And and Or in Logic 1/17/2014 Given a plane and a line in the plane, there exists a point in the plane that is not on the line.

15 12.2: And and Or in Logic 1/17/2014 All lines contain at least 2 points.

16 12.2: And and Or in Logic 1/17/2014 Negating Quantifiers What is the negation of this statement? There exists an angle whose measure is less than 90 degrees.

17 12.2: And and Or in Logic 1/17/2014 What is the negation of this statement? All angles have 2 sides.

18 12.2: And and Or in Logic 1/17/2014 What can you say about the negation of a there exists statement?

19 12.2: And and Or in Logic 1/17/2014 What can you say about the negation of an all or every statement.

20 12.2: And and Or in Logic 1/17/2014 Write the negations of the statements below. There exists a smallest real number. There exists a 2 sided polygon.

21 12.2: And and Or in Logic 1/17/2014 Write the negations of the statements below. All triangles are polygons. Every mammal is a dog.

22 Identify the negation of the statement below. No quadrilaterals have congruent angles and congruent sides. A. All quadrilaterals have congruent angles and congruent sides. B. Squares have congruent angles and congruent sides. C. Rectangles have congruent angles but not congruent sides. D. There exists a quadrilateral with congruent sides and congruent angles. E. There does not exist a quadrilateral with congruent sides and angles. 12.2: And and Or in Logic 1/17/2014

23 12.2: And and Or in Logic 1/17/2014 Construct a truth table for (p and q) or r

24 12.2: And and Or in Logic 1/17/2014 Complete a truth table for ~(p and q) and a separate truth table for ~p or ~q

25 12.2: And and Or in Logic 1/17/2014 ~(p and q) is truth functionally equivalent to ~p or ~q.

26 12.2: And and Or in Logic 1/17/2014 Assignment: pages , # (all).


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