Thinking Mathematically

Compound Statements and Connectives

“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.”

Examples“Miami is a city in Florida” is a true statement.“Atlanta is a city in Florida” is a false statement.“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.

“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.

“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.

“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

“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.

Symbolic Logic

Statements of Logic

Name Symbolic Form

Negation ~p

Conjunction p/\q

Disjunction p\/q

Conditional p q

Biconditional p q