Thinking Mathematically

1. Thinking Mathematically Compound Statements and Connectives

2. Examples “Miami is a city in Florida” is a true statement. “Atlanta is a city in Florida” is a false statement. “Compound” Statements Simple statements can be connected with “and”, “Either … or”, “If … then”, or “if and only if.” These more complicated statements are called “compound.” “Either Miami is a city in Florida or Atlanta is a city in Florida” is a compound statement that is true. “Miami is a city in Florida and Atlanta is a city in Florida” is a compound statement that is false.

3. “And” Statements When two statements are represented by p and q the compound “and” statement is p /\ q. p: Harvard is a college. q: Disney World is a college. p/\q: Harvard is a college and Disney World is a college. p/\~q: Harvard is a college and Disney World is not a college.

4. “Either ... or” Statements When two statements are represented by p and q the compound “Either ... or” statement is p\/q. p: The bill receives majority approval. q: The bill becomes a law. p\/q: The bill receives majority approval or the bill becomes a law. p\/~q: The bill receives majority approval or the bill does not become a law.

5. “If ... then” Statements When two statements are represented by p and q the compound “If ... then” statement is: p  q. p: Ed is a poet. q: Ed is a writer. p  q: If Ed is a poet, then Ed is a writer. q  p: If Ed is a writer, then Ed is a poet. ~q  ~p: If Ed is not a writer, then Ed is not a Poet

6. “If and only if” Statements When two statements are represented by p and q the compound “if and only if” statement is: p  q. p: The word is set. q: The word has 464 meanings. p  q: The word is set if and only if the word has 464 meanings. ~q  ~p: The word does not have 464 meanings if and only if the word is not set.

7. Symbolic Logic Statements of Logic Name Symbolic Form Negation ~p Conjunction p/\q Disjunction p\/q Conditional p  q Biconditional p q