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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
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 logic1
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 logic2
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 logic3
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 logic4
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 logic5
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 logic6
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 logic7
Section 2-2: Logic

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


Section 2 2 logic8
Section 2-2: Logic

  • Homework:

    Pages 103-104, #11 – 29 odd


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