Set Theory — Venn Diagrams

import java.util.HashSet;
import java.util.Set;

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

    // Creates an empty set of integers
    Set<Integer> numSet = new HashSet<>();
    System.out.println(numSet.size());  // → 0 (empty)

    numSet.add(5);                       // Adds 5
    System.out.println(numSet.size());  // → 1

    numSet.add(6);                       // Adds 6
    System.out.println(numSet.size());  // → 2

    numSet.add(5);                       // Tries to add 5 again
    System.out.println(numSet.size());  // → 2 (UNCHANGED! Set ignores duplicates)

    System.out.println(numSet.add(4)); // → true  (4 was new, added)
    System.out.println(numSet.size());  // → 3

    System.out.println(numSet.add(4)); // → false (4 already existed, rejected)
    System.out.println(numSet.size());  // → 3 (still 3)

    // Prints the entire set — order may vary!
    System.out.println(numSet);         // → [4, 5, 6]
  }
}

// Simple class with two attributes
public class CoolClass {
    int value;        // a number
    String text;      // a text

    public CoolClass(int value, String text) {
        this.value = value;
        this.text = text;
    }
}

// Creating objects with the SAME values
CoolClass object1     = new CoolClass(1, "One");
CoolClass object2     = new CoolClass(2, "Two");
CoolClass objectOther1 = new CoolClass(1, "One"); // same value as object1!

Set<CoolClass> coolSet = new HashSet<>();
System.out.println(coolSet.size());    // → 0

coolSet.add(object1);
coolSet.add(objectOther1);              // SAME value, but different object
System.out.println(coolSet.size());    // → 2 (!!) — Shouldn't it be 1?

// ⚠ WARNING: Without overriding equals() and hashCode(),
// Java compares REFERENCES (memory address), not content.
// object1 and objectOther1 have equal values but are different
// objects → the Set treats them as "different".