Free and Bound Variables

In this class, We discuss Free and Bound Variables.

The reader should have prior knowledge of universal and existential quantifiers. Click Here.

We take an example and understand free and bound variables.

Example:

All men will die

The above statement is written as (∀x)(M(x) -> D(x))

In the above equation, x is a bounded variable.

The variable x is quantified using universal quantification.

Variables that are quantified are bounded.

Example 2:

Suresh is a man.

The above statement is written as M(s).

The variable s is a free variable.

The scope of the variable belongs to the equation next to the quantifier.

Examples:

∀x(P(x,y)) Here, x is bound variable and y is free variable.

∀x(P(x) -> Q(x)) Here x is a bound variable.

∀x(P(x) -> ∃y R(x,y)) Her x and y are bound variables.