De Morgan's laws

To negate a compound condition, negate each part and swap the operator.

Proving equivalence with a truth table

Two expressions are equivalent if they match for every combination of inputs. With two booleans there are only four rows to check.

boolean[] vals = {true, false};
for (boolean a : vals) {
  for (boolean b : vals) {
    System.out.println((!(a && b)) == (!a || !b));
  }
}

true
true
true
true

Comparing object references

== and != on references ask "same object?" Comparing with null asks "does this variable refer to any object?". Many classes provide an equals method that compares objects by their contents instead.

String a = new String("cat");
String b = new String("cat");
String c = null;
System.out.println(a != b);
System.out.println(a.equals(b));
System.out.println(c == null);

true
true
true