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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.

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Review

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  1. Review • Find a counter example for the conjectureGiven: JK = KL = LM = MJConjecture: JKLM forms a square

  2. Logic Geometry Unit 9, Day 2 Mr. Zampetti

  3. Objective • To determine the truth values of conjunctions and disjunctions

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

  5. 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

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

  7. 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.

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

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

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

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

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

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

  14. Example • p: The marking period ends on a Fridayq: 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

  15. Example • Givenp: math is funq: 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.

  16. Homework • Work Packet: Logic

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