Discrete Mathematical Structures by Pearson

4-24 Discrete Mathematical Structures

Note 4.4 P(x) is not a proposition but an expression because it involves a variable x that

cannot assign any truth value to P(x). However, if x is replaced by a particular object, it

becomes a proposition. The set of all values that x can assume is called the universe of

discourse.

A predicate may contain two or more variables. A predicate containing two variables x and y

denoted by P(x, y) is called a binary predicate. If a predicate contains n variables, it is called an

n-ary predicate.

From the above discussion, it is clear that P(x) becomes a proposition function in the sense that

for a particular value of x, it becomes a statement. Similarly, P(x, y) will become a proposition

for particular values of ...