Don't Panic: Boolean Logic

Boolean logic is the small machinery of true and false. It gives computing a way to say when a condition holds, when a rule should pass, and when a circuit output should change. The machinery is small enough to fit on a napkin. The surprises arrive when people assume the napkin checked every row by itself.

The basic parts are propositions, which are statements that can be true or false, and operators such as NOT, AND, OR, and XOR. NOT reverses a value. AND requires both inputs. OR requires at least one input. XOR is the fussy cousin that accepts exactly one input and refuses the both-true case. This is why the word either causes so much trouble in meetings.

A truth table is the antidote to guesswork. It lays out every possible input pattern, then pins an output beside each pattern. Two propositions produce four rows. Three produce eight. Once the table exists, the expression has fewer places to hide. If two expressions should be equivalent, compare their final columns row by row rather than trusting one friendly example.

Grouping matters because compound expressions form a tree. (A OR B) AND C is not the same rule as A OR (B AND C). Parentheses are cheap and readers are expensive, so write the grouping down. The same applies when moving NOT through a group: De Morgan's laws swap AND with OR as the negation moves inward. Forget the swap and you have changed the rule, not simplified it.

Software adds local customs. Many languages short-circuit AND and OR, so the right side may not run. Some convert other values to truth values. Python's and and or can return an operand rather than a Boolean. SQL can add unknown. Bitwise operators work on bits, not truth conditions. Boolean logic gives you the skeleton; the host language supplies some of the bones' less charming legal clauses.

Start with the Practice Reference if you need a method. It gives the formulas, row counts, and rewrite checks. Then do the Exercise: build the access-rule table and verify the denial condition. Use the Cheatsheet when you forget whether OR includes both true. It does. It absolutely does.

Don't Panic: Boolean Logic

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