## Welcome to Discrete Math

#### Andy Novocin

## The first rule of Discrete Math

## 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

## Mathematical Statments

### Can be assigned a truth value (true or false)

## Examples of Statements

- Every integer is a perfect square
- \(x\) is an even number
- If it snows I will wear boots

## Examples of Non Statements

- What is your favorite number?
- Suppose that \(x\) is even.

## 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?