Compound Boolean Expressions

AND and OR

• Combine conditions with && (logical AND 逻辑与) and || (logical OR 逻辑或).
• a && b is true only when both are true.
• a || b is true when at least one is true.
• "Is the number between 1 and 10?" → x >= 1 && x <= 10.

NOT reverses

• ! (logical NOT 逻辑非) flips a Boolean: !true is false, !false is true.
• !(x > 5) is true exactly when x is not greater than 5.
• NOT applies to the expression right after it — use parentheses for clarity.
• Double negation cancels: !!a equals a.

Truth table for &&, || and !, with short-circuit evaluation 短路求值

Short-circuit evaluation

• && and || stop as soon as the answer is known — this is short-circuit evaluation.
• For a && b: if a is false, the result is false and b is never evaluated.
• For a || b: if a is true, the result is true and b is skipped.
• This lets you guard: x != 0 && 10 / x > 2 avoids dividing by zero.

Truth tables and parentheses

• A truth table lists every combination of inputs and the expression's result.
• With two variables there are $4$ rows; build one to check tricky logic.
• Use parentheses to make precedence explicit: (a && b) || c.
• Without them, && binds tighter than || — a common source of confusion.