Boolean Expressions and Relational Operators

A computer branches by asking a yes-or-no question, and Java represents that answer as a boolean: true or false, nothing in between. The six relational operators give you ways to ask that question of numbers: == and ≠ test equality and inequality, while <, >, ≤, and ≥ test order. Picture each one splitting the number line into two regions — x > 5 marks everything above 5 as true and everything else false; x ≤ 5 flips which side counts. Whatever condition sits inside an if or a while must boil down to one of these true/false values.

Order of operations matters here just like in arithmetic: Java finishes all the arithmetic before it compares anything. In (q·3 + r) % 3 == 1, Java computes q·3 + r, then takes that result mod 3, and only then compares the leftover to 1. Relational operators always sit at the end of that chain, checking a finished number against another finished number.

This topic sets up everything else in the unit: if-statements choose a branch based on a boolean expression, while and for loops keep running as long as one stays true, and compound conditions in the next topic glue several of these together with && and ||. Get comfortable with what makes an expression boolean now, because every branch and every loop condition after this is built from exactly these pieces.