2 Logic What is Logic? It is our ability to reason. It is the foundation of sound thinking.
3 Where do we start?I start with the question:What is a sentence?Every good sentence needs a noun or subject, an action word or a verb and an object or the completion of the idea of the sentence.
4 How is a mathematical sentence different from an grammatical sentence? A mathematical sentence has a certain truth value. It is called a closed sentence.A sentence whose truth value is uncertain is called an open sentence.
5 NegationThe negation of a sentence changes the truth value of the original sentence.It is represented by the symbol ~.If p represents my sentencethen ~p represents it’s negation.
6 Try This In the space provided write a sentence in words. Then write the negation of that sentence in words.
7 Logical ConnectorsA conjunction connects two simple sentences using the word “and “ to make a compound sentence.Given the two simple sentencesSara goes swimming.Tom is a life guard.The conjunction would beSara goes swimming and Tom is a life guard
8 Logical Connectors with symbols The word And is represented by the symbol ExampleLet p represent: Sara goes swimming.Let q represent: Tom is a life guard.Sara goes swimming and Tom is a life guard.Would be represented by:pq
9 The compound sentence p q is only true when both individual sentences are true. F
10 Disjunction Connective A disjunction connects two simple sentences using the word “or “ to make a compound sentence.Given the two simple sentencesSara will studySara goes to the moviesThe compound sentence would beSara will study or Sara goes to the movies
11 Using Symbols The connector “or” is represented by the symbol “.” Example:Let p represent: Sara will studyLet q represent: Sara goes to the moviesSara will study or Sara will go to the movies. represents:p q
12 The disjunctionp q is only false when both p and q are false.pqp qTF
13 A conditional is a compound sentence usually formed by the words if… A conditional is a compound sentence usually formed by the words if….then to combine 2 simple sentences. The is used to represent if…then.Given the simple sentencesJohn studiesJohn gets good gradesThe compound sentence would be:If John studies then John gets good grades.
14 Using Symbols A conditional statement is also called an implication p implies q.Let p represent: John studiesLet q represent: John gets good gradesIf John studies then John gets good grades.Represent by: p q
15 In a conditional statement the p sentence is called the hypothesis or the premise and the q sentence is called the conclusion.
16 The conditional statement is only false when a true hypothesis implies a false conclusion. qp qTF
17 Homework In the text book Pg. 41 Numbers 48-61 Pg. 47 Numbers 13-20