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Section 2-2: Logic

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- 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.

- Truth Value: The truth or falsity of a statement.
- Example: p: Detroit is a city in Michigan.
- The above statement is True.

- 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.

- 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.

- Conjunction: a compound statement formed by joining two or more statements with the word and.
- Symbols: p ^ q

- Disjunction: A compound statement formed by joining two or more statements with the word or.
- Symbols: p V q

- 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

- A convenient method for organizing the truth values of statements is to use a truth table.

- Homework:
Pages 103-104, #11 – 29 odd