Symbolic Representation
What is the symbol for "OR" and what is the symbol for "AND"
OR : v
AND : ^
Yes or No: both statements in an "AND" statement must be true
~(~p) = ?
p
What is the symbol for negation
~
What does commutative mean and what operators are commutative?
you can change the order of the operators in the problem and it will not affect the answer
AND and OR are both commutative
List the 6 symbolic representations covered in the lecture
Name, variable, negation, AND, OR, exclusive OR
Explain what and inclusive "OR" statement is and explain what an exclusive "OR" statement is
inclusive : at least one statement is true, both could be true
exclusive : exactly one statement is true
What are DeMorgan's Laws
1. ~ (p ^ q) = (~p) v (~q)
2. ~ (p v q) = (~p) ^ (~q)
Define what a negation statement is
The opposite of the truth value
What does associative mean and what operators are associative?
the way in which operators are grouped in a problem does not change the answer
AND and OR are both associative
Put the following statement into symbolic form :
Michael went to Target, and he studied for his exam.
(show all work)
p = Michael went to Target
q = Michael studied for his exam
p ^ q
What is another word that could be used in place of AND
But
Negate the following statement in (use English not symbols) :
Tony cooked dinner, but he did not make pasta.
Tony did not cook dinner, or he did make pasta.
Can a negation be used in every possible scenario
Yes
What are the order of operations
1. Negation
2. AND
3. OR
(if there is a tie work left to right)
Explain what the Comma BUT Rule is
A comma followed by "but" separates the compound sentence into two parts as if parentheses surrounded both halves
What is the word that is placed with "or" in an exclusive formal "OR" mathematical statement
either
Neither p nor q means what
~p ^ ~q
Give an example of a negation
John went to the park
Negation: John did not go to the park
add parentheses where appropriate to p v q ^ r
p v (q ^ r)
Put the following statement into symbolic form :
Jackie brushed, or teeth or she showered, but she did not make her bed.
(show all work)
p = Jackie brushed her teeth
q = Jackie showered
r = Jackie made her bed
(p V q) ^ ~ r
"AND" is a ______ operation on statements
binary
By DeMorgan's Laws, what does ~p ^ ~q equal
~ (p v q)
Negate this statement: All vegetarians eat carrots
Some vegetarians eat carrots
Write the following statement symbolically :
Erin went to her math class or she read a book, but she did not do her homework.
p = Erin went to her math class
q = Erin read a book
r = Erin did not do her homework
(p v q) ^ r