Review Find a counter example for the conjecture Given: JK = KL = LM = MJ Conjecture: JKLM forms a square.

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Presentation transcript:

Review Find a counter example for the conjecture Given: JK = KL = LM = MJ Conjecture: JKLM forms a square

Logic Geometry Unit 9, Day 2 Mr. Zampetti

Objective To determine the truth values of conjunctions and disjunctions

Definition Statement – a sentence that is either true or false. Example: There are 30 desks in the room.

Definition Truth value – the truth or falsity of a statement Example: Statement Truth Value Albany is the capital of NY. True California is on the East Coast False

Statements Statements are often represented by letters, usually p and q Albany is the capital of NY would be represented by p.

Definition Negation – a statement with the opposite meaning and the opposite truth value. Statement: Albany is the capital of NY. Negation: Albany is not the capital of NY.

Notation If a statement is represented by p, then not p is the negation of the statement Not p is written ~p

Example: Statement: This room is on the second floor. (p) Negation: This room is not on the second floor. (~p)

Definition Compound Statement – the joining of two or more statements. We would use two letters, usually p and q, to represent each statement.

Definition Conjunctions – a compound statement formed by joining two or more statements with and p and q is represented by p ^ q

Example Example: p: Albany is a city in NY q: Albany is the capital of NY p and q: Albany is a city in NY and Albany is the capital of NY.

Definition Disjunction – a compound statement formed by joining two or more statements with or

Example p: The marking period ends on a Friday q: The marking period ends 1/29/10 p or q: The marking period ends on a Friday, or the marking period ends 1/29/10 p or q is represented by p v q

Example Given p: math is fun q: geometry is hard Write: 1. p^q, 2. ~qvp, and 3. ~pv~q 1. Math is fun and geometry is hard. 2. Geometry is not hard or math is fun. 3. Math is not fun or geometry is not hard.

Homework Work Packet: Logic