What is Logic? It is our ability to reason. It is the foundation of sound thinking.
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.
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.
Negation The negation of a sentence changes the truth value of the original sentence. It is represented by the symbol ~. If p represents my sentence then ~p represents its negation.
Try This In the space provided write a sentence in words. Then write the negation of that sentence in words.
Logical Connectors A conjunction connects two simple sentences using the word and to make a compound sentence. Given the two simple sentences Sara goes swimming. Tom is a life guard. The conjunction would be Sara goes swimming and Tom is a life guard
Logical Connectors with symbols The word And is represented by the symbol Example Let 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: p q
The compound sentence p q is only true when both individual sentences are true. pq p q TTT TFF FTF FFF
A disjunction connects two simple sentences using the word or to make a compound sentence. Given the two simple sentences Sara will study Sara goes to the movies The compound sentence would be Sara will study or Sara goes to the movies Disjunction Connective
Using Symbols The connector or is represented by the symbol. Example: Let p represent: Sara will study Let q represent: Sara goes to the movies Sara will study or Sara will go to the movies. represents: p q
The disjunction p q is only false when both p and q are false. pq p q TTT TFT FTT FFF
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 sentences John studies John gets good grades The compound sentence would be: If John studies then John gets good grades.
Using Symbols A conditional statement is also called an implication p implies q. Let p represent: John studies Let q represent: John gets good grades If John studies then John gets good grades. Represent by: p q
In a conditional statement the p sentence is called the hypothesis or the premise and the q sentence is called the conclusion.
The conditional statement is only false when a true hypothesis implies a false conclusion. pq p q TTT TFF FTT FFT
Homework In the text book Pg. 41 Numbers 48-61 Pg. 47 Numbers 13-20 Pg. 58 Numbers 3-10