Predicate

Definition

A predicate is a statement form with one or more variables.

It becomes a proposition when the variables are assigned values.

Example:

Even(x)

This means:

x is even

By itself, it is not yet true or false.

If:

x = 4

then:

Even(4) = true

Predicate = proposition with open variable positions.

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Predicate vs Proposition

A proposition already has a truth value.

Example:

Even(4)

This is true.

A predicate contains a variable.

Example:

Even(x)

This needs a value for x before it can be true or false.

Predicate becomes proposition after substitution.

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Predicates Describe Properties

A predicate can describe a property of an object.

Example:

Human(x)

This says:

x has the property of being human

If:

x = Socrates

then:

Human(Socrates)

is a proposition.

Predicates let logic describe properties.

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Predicates Can Relate Objects

A predicate can also describe a relationship between objects.

Example:

GreaterThan(x, y)

If:

x = 5
y = 3

then:

GreaterThan(5, 3) = true

If:

x = 2
y = 9

then:

GreaterThan(2, 9) = false

Predicates can represent properties or relations.

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Predicate vs Function

A function returns a value or object.

Example:

double(3) = 6

A predicate returns a truth value.

Example:

Even(3) = false

This difference matters because predicates create statements for reasoning.

Function gives a value; predicate gives true or false.

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Final Summary

• A predicate is a statement form with variables.
• A predicate becomes a proposition when variables are assigned.
• Predicates can describe properties.
• Predicates can describe relations between objects.
• A predicate returns true or false after substitution.
• Predicates are different from functions.