---
title: "Unary Predicate in Formal Logic I"
description: "Unary Predicate is a one-place predicate that assigns a property to a single object or subject in Formal Logic I, like P(x) for “x is even.”"
canonical: "https://fiveable.me/formal-logic-i/key-terms/unary-predicate"
type: "key-term"
subject: "Formal Logic I"
unit: "Unit 8"
---

# Unary Predicate in Formal Logic I

## Definition

A unary predicate is a predicate that takes one argument and says whether that object has a property. In Formal Logic I, it is the basic way to write statements about a single subject, like P(x).

## What It Is

A unary predicate in Formal Logic I is a one-place predicate, meaning it takes one object from the domain and says something about that object. If the object has the property, the predicate is true for it. If it does not, the predicate is false for it. That makes unary predicates the simplest building block in predicate logic for talking about individual things.

You can think of it as a labeled test for membership in a category. For example, if P(x) means “x is even,” then P(4) is true and P(5) is false. If M(x) means “x is a mammal,” then M(dolphin) is true. The exact meaning comes from the interpretation you assign to the predicate symbol, not from the symbol itself.

This is different from propositional logic, where whole statements are treated as atomic units. Unary predicates let you break a sentence apart so you can track which object it is about and what property it has. That is why Formal Logic I introduces them right before or alongside quantifiers, since quantifiers need predicates to make general claims like “all x” or “some x.”

A common way to read unary predicates is as properties rather than relations. That means the predicate is attached to one thing at a time. If you write P(a), you are checking whether the individual named by a satisfies property P. If you write P(x), the x is a variable that can stand for any member of the domain.

The notation matters because it lets you build precise logical sentences. Once you know how unary predicates work, you can combine them with negation, conjunction, disjunction, and quantifiers to express more complicated claims without losing track of the object you are talking about. That is the bridge from plain English descriptions to symbolic logic.

A good way to spot a unary predicate is to ask, “How many arguments does this predicate take?” If the answer is one, it is unary. If you start needing two objects, like “x loves y,” you have moved into a different kind of predicate and a different kind of logical structure.

## Why It Matters

Unary predicates show up everywhere you translate English into symbol form, because many everyday claims are really about one thing having one property. In Formal Logic I, that makes them the first step in building and evaluating predicate logic statements without mixing up subjects, properties, and truth values.

They also set up quantifiers. You cannot write a clean universal claim like “all cats are mammals” unless you can first express “is a cat” and “is a mammal” as predicates over the same domain. Unary predicates give you that structure, so you can later test whether a statement should be written with a universal quantifier, an existential quantifier, or a negation.

They matter for proof work too. When you prove or disprove a symbolic statement, you often need to recognize what counts as an instance of a property. For example, if a problem gives you P(a) and then asks whether ¬P(a) follows, you are working directly with a unary predicate and its negation. That kind of move shows up in truth evaluations, translation exercises, and short proof problems.

They also keep you from overcomplicating a sentence. Not every English statement hides a relationship between two things. Sometimes the logic is just about one object being in a class, having a feature, or meeting a condition. Unary predicates are the clean way to represent that.

## Connections

### Predicate

A unary predicate is one type of predicate. The broader term covers any expression that says something about objects in the domain, while the unary version focuses on a single argument. If you can tell the difference between the general category and the one-place case, symbolic translation gets much easier.

### Subject

The subject is the object or individual the predicate is talking about. In a unary predicate like P(x), x is the subject position, and P tells you what property is being checked. Keeping subject and predicate separate helps you translate English sentences without swapping the thing being described with the description itself.

### Quantifier

Quantifiers work on predicates to make broader claims. A unary predicate gives the property, and a quantifier like “for all” or “there exists” tells you how many things in the domain should satisfy it. If you misread the predicate, you will usually misread the quantifier sentence too.

### [binary predicate](/formal-logic-i/key-terms/binary-predicate)

A binary predicate takes two arguments, not one. That is the main contrast with a unary predicate, which only checks a property of a single object. Seeing the difference matters when you translate statements like “x is taller than y,” which cannot be represented as unary because it is a relation, not a one-place property.

## On the AP Exam

A problem set or quiz item will usually ask you to identify whether a symbol like P(x) is unary, translate an English property statement into predicate notation, or evaluate whether a particular object makes the predicate true. You may also be asked to decide whether a sentence is unary or really needs another argument. For example, “is red,” “is prime,” and “is a mammal” are unary, but “is taller than” is not. When you see a symbolic statement, check the number of variables first, then check whether the sentence names a property of one thing or a relation between two things. That habit saves a lot of translation mistakes.

## Unary Predicate vs binary predicate

These are easy to mix up because both are predicate symbols with parentheses. The difference is the number of arguments: a unary predicate takes one object, while a binary predicate takes two. If the sentence needs a relation between two things, like “loves” or “is taller than,” it is not unary.

## Key Takeaways

- A unary predicate is a one-place predicate that says whether a single object has a property.
- In notation, it often looks like P(x), where x is the object being checked and P is the property.
- Unary predicates are the basic bridge from ordinary language into predicate logic, especially before quantifiers enter the picture.
- They are true or false only after you choose a domain and interpretation for the predicate symbol.
- If a sentence needs two objects to make sense, it is not unary, it is a relation with more than one argument.

## FAQs

### What is a unary predicate in Formal Logic I?

A unary predicate is a predicate that takes one argument and says whether that object has a certain property. In Formal Logic I, it is usually written like P(x), where x stands for an individual in the domain. The predicate is true or false depending on whether that individual fits the property.

### How do you tell if a predicate is unary?

Count the arguments. If the predicate talks about just one object, it is unary. If it needs two objects, like “x is taller than y,” then it is not unary. A lot of translation mistakes happen when a relation gets treated like a simple property.

### What is an example of a unary predicate?

“Is even” is a classic example. If P(x) means “x is even,” then P(4) is true and P(5) is false. Other examples include “is a mammal,” “is red,” and “is prime,” as long as each one is being applied to one object at a time.

### How is a unary predicate different from a quantifier?

A unary predicate names the property, while a quantifier tells you how many objects satisfy that property. For example, “x is even” is the predicate, but “for all x” or “there exists an x” changes the claim from a one-object check to a statement about the whole domain.

## Related Study Guides

- [8.1 Predicates, Subjects, and Objects](/formal-logic-i/unit-8/predicates-subjects-objects/study-guide/xq06r0nueK8NbMEc)

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