Combining logic

Are you taking the rain jacket today? You probably think something like: if it rains AND it is cold, then yes. Your weather app thinks the same way, just in conditions: it combines several simple checks with AND, OR and NOT into one decision. You already know these three on their own. Now you will learn to nest them, because that is when programs get really smart.

Combining conditions

AND is only true when both parts are true. OR is true as soon as at least one part is true. NOT flips true and false. From these you build longer expressions: (rain AND cold) OR storm means: jacket on if it rains and is cold, or if there is a storm, no matter how warm. The parentheses show what belongs together.

Who goes first?

Just like multiplication before addition, logic has an order of operations: NOT before AND before OR. So the expression NOT A AND B OR C is read as ((NOT A) AND B) OR C. If you want a different order, you need parentheses. And to fully understand a combined expression, a truth table helps: you write down every combination of the inputs and work out the result for each row. With 2 inputs that is 4 rows, with 3 inputs already 8, because every extra input doubles the number of rows.

The trick with NOT in front

What does NOT (rain AND cold) mean? Careful, popular trap: it does not mean that it is neither raining nor cold. It only means: the combination of both is not the case. So it is not raining, OR it is not cold (or both). This transformation is the De Morgan idea: a NOT in front of parentheses moves onto both parts and turns AND into OR (and the other way around).