Boolean Expressions and De Morgan's Laws

Boolean expressions

A boolean expression evaluates to exactly one of two values, true or false. Relational operators build them from numbers: <, <=, >, >=, ==, !=. Logical operators combine them: && (and), || (or), ! (not).

Short-circuit evaluation

Java evaluates && and || from left to right and stops as soon as the answer is known. In p && q the operand q is evaluated only when p is true; in p || q the operand q is evaluated only when p is false. That is why the guard s.length() > 0 && s.substring(0, 1).equals("A") is safe on an empty string while the same two operands written in the other order throw an exception.

De Morgan's Laws

!(p && q) is equivalent to !p || !q, and !(p || q) is equivalent to !p && !q. Negating a relational operator moves it across the boundary rather than past it: the negation of x < 5 is x >= 5, never x > 5. Two boolean expressions are equivalent when they agree on every row of the truth table, and that table is the only proof the exam accepts.