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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