Dynamically making a field read only using Apex in Salesforce

Sample Code:

Visualforce page:

<apex:page controller="sample">
   
    <apex:form >
   
    <apex:pageBlock>
        <apex:pageBlockSection columns="2">
            <apex:pageblockSectionItem>
                <apex:outputLabel value="State"/>
            </apex:pageblockSectionItem>       
            <apex:pageblockSectionItem>               
                <apex:selectList size="1" value="{!state}">
                    <apex:selectOptions value="{!states}"/>
                    <apex:actionSupport event="onchange" reRender="a"/>
                </apex:selectList>               
            </apex:pageblockSectionItem>
            <apex:pageblockSectionItem>
                <apex:outputLabel value="City"/>
            </apex:pageblockSectionItem>           
            <apex:pageblockSectionItem>
                <apex:selectList size="1" value="{!city}" id="a" disabled="{!bool}">
                    <apex:selectOptions value="{!cities}"/>
                </apex:selectList>
            </apex:pageblockSectionItem>           
        </apex:pageBlockSection>       
    </apex:pageBlock>

    </apex:form>

</apex:page>

Apex Class:

public class sample
{
    public String state {get;set;}
    public String city {get;set;}
    public Boolean bool {get;set;}
   
    public sample()
    {
        bool = true;
    }

    public List<SelectOption> getStates()
    {
        List<SelectOption> options = new List<SelectOption>();
        options.add(new SelectOption('None','--- None ---'));       
        options.add(new SelectOption('TN','Tamil Nadu'));
        options.add(new SelectOption('KL','Kerala'));
        return options;
    }
   
    public List<SelectOption> getCities()
    {
        List<SelectOption> options = new List<SelectOption>();
        if(state == 'TN')
        {      
            options.add(new SelectOption('CHE','Chennai'));
            options.add(new SelectOption('CBE','Coimbatore'));
            bool = false;
        }
        else if(state == 'KL')
        {      
            options.add(new SelectOption('COA','Coachin'));
            options.add(new SelectOption('MVL','Mavelikara'));
            bool = false;
        }
        else
        {
            options.add(new SelectOption('None','--- None ---'));
        }     
        return options;
    }      
}