Go through 2 lists in java

The problem you're having is that for each item in the list DiasSemana you're going through the entire list DiasTRabajo and for each element of the latter print something, whether it worked or not. This is not correct, because in order to determine if in the list DiasTRabajo is the day analyzed according to the list DiasSemana and print whether it worked or not, you must go through it until you find that day, or not, and at that moment, When you finish going through it, you must indicate whether it worked or not. For example:

    boolean found;
    for (String ds : DiasSemana) {

        found = false;
        for (String dt : DiasTRabajo) {
            if (ds.equals(dt)) {
                found = true;
                break;
            }
        }

        if (found) {
            System.out.println("Trabaja : " + ds);
        } else {
            System.out.println("NO Trabaja : " + ds);
        }
    }

If you notice, the variable found used it to put it as true if I find the analyzed day. If when leaving the for nested (the inside) found is true, then indicated that it worked and otherwise indicated that it was not worked and proceed to analyze the next day of the week.

The break I use to finish the execution of the for nested if I find the day.

Guys respect its solution but it is not necessary to go through the two lists with just one stroke, since the ArrayList have the constains method which returns a Boolean value if one of the elements that is passed is in the list to be verified , here my solution:

See Java.Util.ArrayList.contains documentation

import java.util.*;

public class MyClass {
    public static void main(String args[]) {
        ArrayList<String> DiasSemana = new ArrayList<>();
    DiasSemana.add("Lunes");
    DiasSemana.add("Martes");
    DiasSemana.add("Miércoles");
    DiasSemana.add("Jueves");
    DiasSemana.add("Viernes");
    DiasSemana.add("Sábado");
    DiasSemana.add("Domingo");

    ArrayList<String> DiasTRabajo = new ArrayList<>();
    DiasTRabajo.add("Lunes");
    DiasTRabajo.add("Miércoles");
    DiasTRabajo.add("Viernes");
    DiasTRabajo.add("Domingo");

        for (String ds : DiasSemana) {
             System.out.println(DiasTRabajo.contains(ds) ? "Trabaja : " + ds :"NO Trabaja : " + ds);
        }
    }
}

Better with Java8, the code is clearer:

diasSemana.stream().forEach( (d) -> { String laborable = diasTRabajo.contains(d) ? " Trabaja" : " Libra"; System.out.println(d + laborable); });

I did it in the following way with your example:

import java.util.ArrayList;
import java.util.List;

public class MyClass {
public static void main(String args[]) {

    String Dia = "";
    boolean check = false;

    List<String> DiasSemana = new ArrayList<>();
    DiasSemana.add("Lunes");
    DiasSemana.add("Martes");
    DiasSemana.add("Miércoles");
    DiasSemana.add("Jueves");
    DiasSemana.add("Viernes");
    DiasSemana.add("Sábado");
    DiasSemana.add("Domingo");

    List<String> DiasTRabajo = new ArrayList<>();
    DiasTRabajo.add("Lunes");
    DiasTRabajo.add("Miércoles");
    DiasTRabajo.add("Viernes");
    DiasTRabajo.add("Domingo");

        for (String ds : DiasSemana) {
            check = false;
            for (String dt : DiasTRabajo) {
                    if (ds.equals(dt)) {
                        check = true;
                        Dia = ds;
                    } else {
                        Dia = ds;
                    }
            }
            if(check)
            {
               System.out.println("Trabaja : " + Dia); 
            }
            else{
                System.out.println("NO Trabaja : " + Dia);
            }


        }
}
}

Ready.