Computer Science › Math for Programmers
Boolean Logic
AND, OR, NOT and De Morgan's laws.
Also known as: boolean algebra, De Morgan's laws, logic operators
Boolean logic is the algebra of true and false. Three operations build everything else.
| Operation | Symbol | True when |
|---|---|---|
| AND | and, && | both are true |
| OR | or, || | at least one is true |
| NOT | not, ! | the input is false |
A truth table lists every case:
| A | B | A and B | A or B |
|---|---|---|---|
| F | F | F | F |
| F | T | F | T |
| T | F | F | T |
| T | T | T | T |
Useful laws
De Morgan’s laws let you push a NOT through a condition:
not (A and B) == (not A) or (not B)
not (A or B) == (not A) and (not B)# "not (is_member and has_coupon)" is the same as:
(not is_member) or (not has_coupon)Other handy equivalences: not not A == A, A and True == A, A or False == A, and the distributive form A and (B or C) == (A and B) or (A and C).
In code
- Simplify conditions.
if not (x > 5 and y < 3)can read better asif x <= 5 or y >= 3. - Avoid double negatives (
if not is_disabled). Name booleans positively. - Short-circuiting stops evaluation early (short-circuit evaluation).
- Precedence:
andbinds tighter thanor. Use parentheses (operator precedence). - Empty cases:
all([])is true,any([])is false.
Beyond if statements
The same logic drives SQL WHERE clauses (with a third value, NULL, see NULL in SQL), search filters, access rules, feature flags, and digital circuits. Bitwise operators apply it to each bit of a number.