Predicates

So far, we've dealt with statements that are true or false. A predicate is more general: it's an expression that says something about one or more objects, but by itself, it's not yet a statement.

What is a predicate?

A predicate expresses a property or relation. It becomes a statement when we assign a specific value to the variable.

This is the predicate P(x). If x = 7, then the statement is true. If x = 3, then false.

One-variable predicate

This is a predicate that expresses: "x is an even number". If x = 4, then P(x) is true. If x = 5, then P(x) is false.

Two-variable predicate

This expresses a relation: "x is less than y". If x = 2 and y = 5, then R(x,y) is true. If x = 7 and y = 4, then false.

Difference between predicate and statement

• A statement is always true or false.
• A predicate contains variables, so by itself, we can't decide if it's true.
• It becomes a statement only when we substitute a specific value.

Summary

A predicate is an expression that says something about objects. When we specify the values of the variables, the predicate becomes a statement that can be true or false.

Practice Exercise