3.1 Statements and Logical Connectives Flashcards
Connectives
The words and, or, if…then
Exclusive or
When one or the other of the events can take place, but not both
Ex: “You can go to the beach or have ice cream for dinner”
Inclusive or
Implies that one or the other, or both events can take place
Ex: “May I interest you in a cup of soup or a sandwich?”: you can order a cup of soup, a sandwich, or both
If-then statements
Used to relate two ideas
Ex: “If you clean your room, then you may go to the beach”
Statement
A statement can be judged as either true or false
Assigning a truth value
When we label a statement as true or false
Simple statements
Convey one idea
Ex: “The Empire State Building is in New York”
Compound statements
When sentences combine two or more ideas that can be assigned a truth value
Negation
Change a statement to its opposite meaning
Negate
“All are”
“None are”
“Some are”
“Some are not”
“Some are not”
“Some are”
“None are”
“All are”
Translate to logic statement “if you commit a crime, then you will be caught”
If p, then q; where p = you commit a crime and q = you will be caught
Use -> to represent “if, then”
Negation (Symbolized ~, read as “not”)
~p
~(~p) = p
Conjunction (symbolized ^, read as “and”)
Ex:
p = you will perform 5 months of community service
And
q = you will pay a fine of $100 dollars
Represented as: p^q
Disjunction (symbolized v, read as “or”)
Ex:
P: Cameron will take Chemistry
Q: Cameron will take French
“Cameron will not take Chemistry or Cameron will not take French”
Represented as: ~pV~q
Contain more than one connective
Ex: “Pink is a singer (p) or Jennifer Anniston is an actress (q), and Orlando is in Florida”
(p V q) ^ r
