Welcome to Discrete Math

Andy Novocin

The first rule of Discrete Math

Syllabus Link

at math.prof.ninja

How you will feel at first

“The fool looks at the finger that points to the sky.”

You are learning a new language

You are jumping into a new culture

Welcome to the club!

Mathematical Statments

Can be assigned a truth value (true or false)

Examples of Statements

Examples of Non Statements

Exploring the truth value of a statement

Dip our toes in the water. Convince your partner that:

\(x + 1\) is odd for every even integer \(x\).

To really demonstrate the truth of something we need a proof.

Take a look at my friend's blog

Today let's start with the atoms of proofs

Take a statement \(p\) and a statement \(q\).

We can combine them to create a new statement.

Different combinations have different interpretations

Combination Symbols

\(p \land q\) is "\(p\) and \(q\)"

\(p \lor q\) is "\(p\) or \(q\)" (inclusive or)

\(p \to q\) is "If \(p\) then \(q\)"

\(\lnot p\) is "Not \(p\)"

\(\exists x\) is "There exists an \(x\)"

\(\forall x\) is "For all \(x\)"

\( p \iff q\) is "\(p\) if and only if \(q\)"

AND and OR

Combine the statement \(p: x+2 = 3\) with \(q: x \neq 1\) using \(\land\) and \(\lor\)

Which new statement is true?

The rest on the board