Logic

Eric Hoffman

Advanced Geometry

PLHS

Sept. 2007

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

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

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.

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.

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

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

Key Topics• Truth Tables – convenient way to organize truth

values.

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Key Topics

• 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)

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• Homework:

Pgs. 73, 74 18-44 even, 56-72 even

23 problems!!!

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