# Thread: free vs bound variable - predicate calculus

1. ## free vs bound variable - predicate calculus

Hi

I am a new member. As per my understanding, if a variable in a formula does not fall under a quantifer, it is free and if it does, it is bound.

Could you tell me if my understanding correct?

I am currently reading the book "mathmatical logic for computer science" page 106. Please see the attached image or visit

Mathematical logic for computer science - Google Books

a proof has been given which mentions

A'= $\forall$x A1(x)

and then the text: but x is the only free variable in A1 ...........

My question is: is x free? It falls under for all quantifier ...

Sorry for the long question and thank you for your help.

Suzzane.

2. ## Re: free vs bound variable - predicate calculus

Originally Posted by suzanne
Hi A'= $\forall$x A1(x) and then the text: but x is the only free variable in A1 ........... My question is: is x free? It falls under for all quantifier ...
$x$ is free in $A_1(x)$ by hypothesis but not in $\forall xA_1(x)$ . Notice that in the latter case, $x$ always occurs within the scope of the quantifier $\forall x$ .

3. ## Re: free vs bound variable - predicate calculus

Originally Posted by suzanne
I am a new member. As per my understanding, if a variable in a formula does not fall under a quantifer, it is free and if it does, it is bound.

Could you tell me if my understanding correct?
This is correct; however, to be more precise, "free" or "bound" pertain to occurrences of variables. A variable can have both free and bound occurrences in a single formula. In this case, though, bound occurrences should be renamed for clarity.