# Section 2-2: Logic - PowerPoint PPT Presentation

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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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Section 2-2: Logic

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### 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