Question

What are the elements of a proof that there is a unique element such that, where is a propositional function?

Short answer

The predicate and quantifier are the elements of proof.

Step-by-step solution

Introduction

A propositional function or a predicate in propositional calculus is a sentence expressed in a form that would assume the value of true or false, except that there is a variable within the statement that is not defined or described, leaving the statement undecided.

Elements of proof

Explain the elements of a proof that there is a unique element x such thatP (x) where P(x) is a propositional function.

Suppose a declarative statement

X is greater than 3.

If we denote this declarative statement byP (x) where:

~ X is the variable

~ P is the predicate is greater than 3

The declarative statement P(x) is said to be the value of the propositional function P at x.

Once a value has been assigned to the variable x, the declarative statement P (x) becomes a proposition and has a truth value either true or false.

Here, the predicate and quantifier are the elements of proof.