Boolean Expressions: Revision Notes (Computer Science A 2.2)

Recap

A Boolean expression evaluates to true or false. The simplest ones use a relational operator to compare two values.

Operator	Meaning	Works on
`==`	equal to	primitives (values) and references (references)
`!=`	not equal to	primitives and references
`<` `>`	less than, greater than	numeric values
`<=` `>=`	less than or equal to, greater than or equal to	numeric values

The expression 5 > 3 is a complete Boolean expression whose value is true. Its type is boolean.

Key relationships

Idea	Rule
Result type	A relational expression is always `boolean`
Precedence	Arithmetic first (`* / %` then `+ -`), then the relational operator
Words to operators	at least `>=`; at most `<=`; more than `>`; fewer than `<`; exactly `==`; different `!=`
Multiple of k	`n % k == 0`
Storing the result	`boolean isEven = n % 2 == 0;`
Close enough (doubles)	`Math.abs(x - y) < tolerance`

Assumptions

<, >, <=, >= are used only with numeric values.
A condition must be of type boolean: x = 5 is not a condition.
int / int is integer division; if either operand is a double the quotient is a double.

Mistakes to avoid

Writing = where == is meant.
Chaining comparisons such as 3 < x < 9.
Using > when the question says “at least”, or >= when it says “more than”.
Forgetting that 7 / 2 is 3 when both are int.
Testing computed doubles with ==.
Evaluating the relational operator before the arithmetic.

Worked mini-example

Let m = 14 and k = 4. Evaluate each expression on its own.

m / k >= 3: m / k is int division, 14 / 4 = 3, and 3 >= 3 is true.
m % k == 2: 14 % 4 = 2, and 2 == 2 is true.
m / (double) k > 3.5: 14 / 4.0 = 3.5, and 3.5 > 3.5 is false.
m - k * 2 != 6: 14 - 8 = 6, and 6 != 6 is false.

Method: replace each variable by its value, finish the arithmetic on both sides (watching for int division), then apply the relational operator last. If the question uses a boundary word such as “at least”, test the boundary value itself.

Quick self-check

Evaluate 8 % 3 == 2. Answer: 8 % 3 is 2, so 2 == 2 is true.
Evaluate 9 / 2 > 4. Answer: 9 / 2 is the int 4, so 4 > 4 is false.
Write “n is at most 100” as a Boolean expression. Answer: n <= 100.
Why does 1 < y < 5 fail to compile? Answer: 1 < y is a boolean, and a boolean cannot be compared to 5 with <.
Which value does 3 + 4 * 2 >= 11 give? Answer: 3 + 8 = 11, and 11 >= 11 is true.

Full explanations and diagrams are in the Topic 2.2 study guide.