Download Geometry Notes 2.2 Logic Determining Truths Values

Geometry Notes
2.2 Logic
Determining Truths Values
1. __________________________ - a sentence that is either true or false
A. _______________________ of a statement is either true or false (determining if it is true or false)
B. Statements are represented by letters ___ and ____, ____
Example:
p: A rectangle is a quadrilateral
q: A rectangle is a convex
truth value ____
truth value ____
2. ______________ of a statement has the opposite meaning as well as an opposite truth.
A. Negations are represented by the symbol __ p (not p)
Example:
p: A rectangle is not a quadrilateral
q: A triangle never has two acute angles
truth value _____
truth value _____
Compound Statements
1. Two or more statements joined by the word _____ are called ___________________
A. A conjunction is only true when both statements are ______
B. A conjunction is written
1. p ___ q OR
2. p ___ q
Example:
p: A rectangle is a quadrilateral
q: A triangle has two acute angles
1. p ∧ q
2. ~p∧ q
truth value ______
truth value ______
2. Two or more statements joined by the word _____ are called ___________________
A. A disjunction has at least ____ true statement (both statements can be true in a disjunction)
B. A disjunction is written
1. p ___ q OR
2. p ___ q
Example:
p January has 31 days
q: January is a spring month
1. p ∨ q
2. ~p ∨ q
truth value ______
truth value ______
Truth Tables
A way to organize truth values of statements and negations
Truth Table for a conjunction of p and q
1.
List all statements
p
q
p∧q
3. Determine
truth for each
compound
2. List
all
combos
of truth
values
Truth table with a negation ~ p and q
1.
List all statements
p
q
~p
~p ∨ q
4. Determine
truth for each
compound
2. List
all
combos
of truth
values
3. Look at
truth value
of p to
determine
negation