Programming fundamentals: The common Boolean operators AND, OR and NOT

The idea

Boolean operators work on truth values, each of which is either True or False. AND returns True only when both inputs are True, so True AND False is False. OR returns True when at least one input is True, so False OR True is True. NOT reverses a single value, so NOT True is False and NOT False is True. These operators let programs combine conditions, for example checking whether a user is logged in AND has admin rights, or whether a score is below zero OR above one hundred. In an exam, you may be asked to complete a truth table, evaluate an expression, or write a condition using AND, OR and NOT. Work through each operator in turn, applying brackets first, then NOT, then AND, then OR, and record the final truth value clearly.

What earns the marks

• AND is a binary operator that produces True only when both of its operands are True; if either operand is False, the result is False. For example, True AND False evaluates to False.
• OR is a binary operator that produces True when at least one operand is True; it produces False only when both operands are False. For example, False OR True evaluates to True.
• NOT is a unary operator that negates a single Boolean value, turning True into False and False into True. For example, NOT False evaluates to True.
• Boolean operators are used in selection and iteration to combine or invert conditions, such as while not finished or if age >= 18 and has_ticket.
• A truth table lists every combination of input values and the resulting output, which helps verify the behaviour of an expression. For two inputs, there are four rows: both False, first True, second True, and both True.

Common mistakes and how to put them right

• Treating AND as if it returns True when either input is True.

  Put it right: AND requires both inputs to be True. For example, True AND False is False, not True.

• Confusing OR with exclusive or, expecting False when both inputs are True.

  Put it right: OR returns True when at least one input is True, including when both are True. For example, True OR True is True.

• Applying NOT to two values, as in NOT True AND False, without deciding which part is negated.

  Put it right: NOT applies to one value or a bracketed expression, so use brackets to make the intended meaning clear. For example, NOT (True AND False) is True, whereas (NOT True) AND False is False.

Exam tips

• Write out each intermediate truth value when evaluating a compound expression, so your working can be followed and checked.
• Use brackets in written conditions to make the order of evaluation explicit, especially when NOT is combined with AND or OR.
• Check a completed truth table by testing one row where all inputs are False and one row where all inputs are True, as these often reveal errors quickly.