1. Logic Eric Hoffman Advanced Geometry PLHS Sept. 2007

2. Key Topics Statement – any sentence that is either true of false, but not both –Often represented by using a letter such as p or q Truth Value – the truth of falsity of a statement Negation – the negation of a statement has opposite meaning as well as opposite truth value –Ex. : p: Perry is a town in Kansas (~p) not p: Perry is not a town in Kansas

3. Key Topics Compound Statement – when two or more statements are joined by using the words “and” or “or” Conjunction – compound statement formed when using the word “and” to join two or more statements p Λ q read: p and q Disjunction – compound statement formed when using the word “or” to join two or more statements p V q read: p or q

4. Key Topics Conjunction Truth Values : for a conjunction to be true, both p and q have to be true. –Ex. : Perry is a town in Kansas and Perry is a smaller town than Topeka. p : Perry is a town in Kansas q : Perry is a smaller town than Topeka Both true so p Λ q is true.

5. Key Topics Conjunction Truth Values : p : Perry has a population of 50,000 people. q : Perry is a town in Kansas. q: is true, but p: is not true, so p Λ q is not true.

6. Key Topics Disjunction Truth Values – for a disjunction to be true either p has to be true, q has to be true, or both are true p: Triangles have three sides q: Equilateral triangles have 3 congruent sides r: Scalene triangles have 2 congruent sides What are the truth values for the following: p V q, p V r, q V r, p Λ q, q Λ r, p Λ r

7. Key Topics Truth Values – the negation of a statement always has the opposite truth value p: Triangles have three sides True ~ p: Triangles do not have three sides False q: Equilateral triangles have 3 congruent sides r: Scalene triangles have 2 congruent sides What are the truth values for the following: p V ~ q, ~ p V r, ~ q V r, p Λ ~ q, ~ q Λ r, p Λ ~ r

8. Key Topics Truth Tables – convenient way to organize truth values.

9. Key Topics

11. In Class Example : p : A rectangle has 4 congruent angles q : A rectangle is a square r : A square is a rectangle Construct the truth table for: (q V ~r) Λ (p Λ ~q) Key Topics

12. Homework: Pgs. 73, 74 18-44 even, 56-72 even 23 problems!!! Key Topics