3.1 Statements and Quantifiers 3.2 Truth Tables.  A statement is a declarative sentence that is either true or false.  Examples: Mr. Healey is my math.

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Presentation transcript:

3.1 Statements and Quantifiers 3.2 Truth Tables

 A statement is a declarative sentence that is either true or false.  Examples: Mr. Healey is my math teacher. It is sunny today in Narragansett = 10 The Patriots lost this past weekend.

 Paint the wall.  Paul Pierce is better than Ray Allen.

 May be formed by combining two or more statements using logical connectives.  And, or, not, if…then are examples of connectives.

 The negation of a true statement is false.  The negation of a false statement is true.

 “Tom Jones has a red car.”  The negation would be: “Tom Jones does not have a red car”  “The sun is a star”  The negation would be: “The sun is not a star.”

ConnectiveSymbolType of statement AND Λ Conjunciton OR V Disjuction Negation ~

 Let p represent “It is 80 degrees today” and let q represent “It is Tuesday.”  Write each symbolic statement in words.  p V q  ~p Λ q  ~(p V q)  ~(p Λ q)

StatementNegation All do.Some do no. (Equivalently: Not all do.) Some do.None do. (Equivalently: All do not.)

 Truth tables give every outcome for specific compound statements.  Today we will look at AND, OR, and the NEGATION truth tables.

 Example: I went to Florida and saw a Red Sox game. pq p Λ q TTT TFF FTF FFF

 I own a Nissan or I own a Ford. pqp V q TTT TFT FTT FFF

p~p TF FT

 P , 23-35odd, 43,4447,49,52, 57, 58, 59,  P : 7-15