Section 2-2: Logic

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# Section 2-2: Logic - PowerPoint PPT Presentation

Section 2-2: Logic. Statement : Any sentence that is either true or false, but not both. Statements are often represented using a letter such as p or q. Example: p : Detroit is a city in Michigan. Section 2-2: Logic. Truth Value : The truth or falsity of a statement.

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Presentation Transcript
Section 2-2: Logic
• Statement: Any sentence that is either true or false, but not both.
• Statements are often represented using a letter such as p or q.
• Example: p: Detroit is a city in Michigan.
Section 2-2: Logic
• Truth Value: The truth or falsity of a statement.
• Example: p: Detroit is a city in Michigan.
• The above statement is True.
Section 2-2: Logic
• Negation: A statement that has the opposite meaning as well as an opposite truth value.
• Not p: Detroit is not a city in Michigan.
• In this case, the above statement has a truth value of False.
• Not p is shown as ~p.
Section 2-2: Logic
• Compound Statement: Two statements that are joined.
• p: Detroit is a city in Michigan.
• q: Detroit is the capital of Michigan.
• p and q: Detroit is a city in Michigan and Detroit is the capital of Michigan.
Section 2-2: Logic
• Conjunction: a compound statement formed by joining two or more statements with the word and.
• Symbols: p ^ q
Section 2-2: Logic
• Disjunction: A compound statement formed by joining two or more statements with the word or.
• Symbols: p V q
Section 2-2: Logic
• Example:

p: One foot is 14 inches

q: September has 30 days

r: A plane is defined by three noncollinear points.

p^q ~q^r

r^p ~p ^ r

pVqqVr

Section 2-2: Logic
• A convenient method for organizing the truth values of statements is to use a truth table.
Section 2-2: Logic
• Homework:

Pages 103-104, #11 – 29 odd