Logical Operators NOT, AND, and OR

Each operator does one specific job. NOT flips a single value: true becomes false, false becomes true. AND looks at two values and gives true only when both are true; any false makes the whole thing false. OR gives true when at least one value is true, and only fails when both are false. These rules are exactly why an alarm wired with AND (motion sensor AND door sensor) stays quiet unless both trip, while one wired with OR (motion sensor OR door sensor) goes off if either does. AND is strict and demanding; OR is generous and easily satisfied.

You build a truth table by listing every combination of true/false for the inputs, then applying the rule row by row. For A AND (B OR NOT A), you work inside out: compute NOT A, then B OR NOT A, then AND that with A. With two inputs there are four rows to check, and the final column is the answer for every possible case.

This connects directly to branching: an if statement's condition is a Boolean expression, often built from AND, OR, and NOT, and the program takes different paths depending on what that expression evaluates to. Getting these operators right is also what makes De Morgan's law work, which lets you rewrite a negated compound condition into an equivalent one, something that matters when simplifying or debugging conditions in code.