# CSCE 222 Chapter 1.3

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## Predicates

A "function" that takes one or more inputs and evaluates to either **true** or **false**

- EX: Let ; ;

## Quantifiers

- Higher precedence than all logical operators
- Distribute across parenthesized terms:

### Universal Quantification

If a predicate is true for all values of in the domain,

To be contradicted, we need to find only one value of such that is false.

### Existential Quantification

If a predicate is satisfiable for at least one value of in the domain,

To be contradicted, every value of has to be false.

### Variable Binding

A variable is **bound** if a quantifier is used on that variable. For example, in , is bound, but is **free** (not bound). To fix this, we would write .

## Negating Quantifiers

"Every student in your class has taken a course in calculus" could be written as .

Negation would be "There is a student in your class who has not taken a course in calculus", which could be written