Lecture: TTh 3:30-4:45
Discussions: MW Various Times
Regrades must be within 3 days
Note about Quizzes
Note about homeworks
Ask Questions
Make Friends
Start Projects Early
Feel Emotions
Expect to get things wrong
Statement: a declarative sentence with a truth value
Statement: a declarative sentence with a truth value
ie. A sentence that is either true or false, but not both
ie. A sentence that is either true or false, but not both
Aristotle's work founded Aristotelian logic
ie. A sentence that is either true or false, but not both
Aristotle's work founded Aristotelian logic
Discrete Math has no applications to CS
Discrete Math has no applications to CS
\[2 + 2 = 4\]
\[2 + 2 = 4\]
\[1 + 1 = 0\]
\[1 + 1 = 0\]
They are not opinions
They are not opinions
C is better programming language than Java
They are not meaningless
They are not meaningless
Colorless green ideas sleep furiously
Must be defined
Must be defined
\[x > 30\]
Must be defined
\[x > 30\]
Must be defined
let \(x\) be the number of students in class
\[x > 30\]
Statements variables are denoted as a lowercase letter
Statements variables are denoted as a lowercase letter
\[x > 30\]
Statements variables are denoted as a lowercase letter
\(y\) = there are more than 30 students in the class
Debate: do they need to be verifiable?
Debate: do they need to be verifiable?
There is a teapot that orbits the sun between Earth and Mars
Statements can be modified
Negation
\(p: 2 + 2 = 4\)
~\(p:\)~\(( 2 + 2 = 4)\)
Note: these all be negation: \({\sim},\neg,\bar p\)
~\(p:\)~\(( 2 + 2 = 4)\)
\(p\) is true and ~\(p\) is false
\(p\) is true and ~\(p\) is false
\(a\): \(p\) is true; \(b\): ~\(p\) is false
\(p\) is true and ~\(p\) is false
\(a\): \(p\) is true; \(b\): ~\(p\) is false
\(a\) and \(b\)
\(a\): \(p\) is true; \(b\): ~\(p\) is false
\(a\) and \(b\)
Conjunction
\(a\): \(p\) is true; \(b\): ~\(p\) is false
\(a\) \(\land\) \(b\)
Conjunction
Disjunction
\(p \lor q\)
\(p \lor q\)
True when \(p\) or \(q\) or both is true
\(p: 2 + 2 = 4\)
\(q: 2 + 3 = 4\)
\(p: 2 + 2 = 4\)
\(q: 2 + 3 = 4\)
\(p \lor q\)
\(p: 2 + 2 = 4\)
\(q: 2 + 3 = 4\)
\(p \lor q\)
(I like Windows)\(\lor\)(I love watching ads)
(I like Windows)\(\lor\)(I love watching ads)
(I am 43 years old)\(\lor\)(I am in Maryland right now)
(I am 43 years old)\(\lor\)(I am in Maryland right now)
(I love chocolate)\(\lor\)(I still play with legos)
(I love chocolate)\(\lor\)(I still play with legos)
(I love chocolate)\(\lor\)(I still play with legos)
Statements are true or statements are false
There is an order of operations
Please: just use parenthesis
Conditionals also exist
Conditionals also exist
If I throw a ball, then the window will break
Conditionals also exist
\(p\): I throw a ball; \(q\): the window will break
Conditionals also exist
\(p\): I throw a ball; \(q\): the window will break
\(p \Rightarrow q\)
Conditionals also exist
\(p\): I throw a ball; \(q\): the window will break
\(p \Rightarrow q\)
Important: not causal