2.2 Boolean Expressions

What you need to know

• Relational operators: ==, !=, <, >, <=, >=. They produce a boolean.
• == compares values for primitives and references for objects. To compare object contents (Strings especially) use .equals().
• A boolean variable can hold the result: boolean ok = score >= 70;. Then if (ok) — no need for if (ok == true).
• Arithmetic is evaluated before relational operators: x + 1 > y * 2 computes both sides first.
• Comparing doubles with == is unreliable due to round-off; the exam usually avoids it or uses a tolerance.
• != means "not equal"; for Strings, use !a.equals(b).

Worked example

int a = 5, b = 10;
boolean p = a * 2 == b;          // true
boolean q = a != b;              // true
String s1 = "hi";
String s2 = new String("hi");
boolean r = s1 == s2;            // false (different objects)
boolean t = s1.equals(s2);       // true  (same contents)

Going deeper

The nuance, edge cases, and connections that turn a 3 into a 5.

• For primitives, == and != compare values. 5 == 5 is true. For doubles, exact equality is unreliable due to representation error; compare with a tolerance (Math.abs(a - b) < 0.0001) in real code. The exam avoids the issue.
• For references, == compares addresses. Two separate objects are never == even with identical contents. Use .equals for content comparison — String defines it by contents; your own classes inherit Object's version (address comparison) unless you write your own.
• Relational operators have lower precedence than arithmetic, so a + b > c * d does both computations first. They have higher precedence than logical operators (&&, ||), so a > b && c < d compares first, then ands.
• A relational expression is a boolean value — it can be stored, returned, passed as an argument. return x > 0; is cleaner than if (x > 0) return true; else return false; and the exam accepts both.
• != on booleans is XOR: a != b is true when exactly one is true.
• Comparing a boolean to true (if (done == true)) is redundant; if (done) means the same. Comparing to false is if (!done).

Mistakes that cost points

• String comparison with ==. The most common wrong answer in Unit 2. Always .equals.
• Chaining comparisons. 1 < x < 10 doesn't compile (the first comparison yields a boolean, which can't be compared to 10). Write 1 < x && x < 10.
• Using = in a condition. Compile error for non-booleans.

Practice questions

Written in the style of the real exam. Try each one before revealing the answer.