Thinking Mathematically Compound Statements and Connectives.
-
Upload
mervin-johnston -
Category
Documents
-
view
220 -
download
4
Transcript of Thinking Mathematically Compound Statements and Connectives.
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