choosing a logical operator

how to choose an operator

this guide helps you select the right logical operator based on the outcome you want to achieve. instead of asking “what does AND do?”, this page answers the question, “which operator should i use if i need…?”

use the summary table below to find the operator that fits your needs.

outcome to operator cheat sheet

use this table as a quick reference to find the operator that matches your goal.

if you need the result to be true when…	use this operator	example use case
all of your conditions are true	conjunction (and)	`user.is_logged_in and user.has_permission`
at least one of your conditions is true	disjunction (or)	`is_admin or is_editor`
your two conditions have the same value (both T or F)	biconditional (iff)	`feature_enabled == user_setting_is_true`
a true premise leads to a true conclusion	implication (if…then)	`if is_raining then ground_is_wet`
you need to invert a single condition’s value	negation (not)	`not user.is_banned`

detailed scenarios

goal: all conditions must be met

scenario: you are granting access to a secure resource. the user must be logged in, have the correct permissions, and be on a trusted network.
operator: conjunction (and)
logic: is_logged_in AND has_permission AND is_trusted_network
outcome: the expression is only True if all three individual conditions are True.

goal: any one of several conditions is enough

scenario: you are checking if a user is eligible for a discount. they qualify if they are a student, a senior, or a veteran.
operator: disjunction (or)
logic: is_student OR is_senior OR is_veteran
outcome: the expression is True if the user fits into any one of those categories.

goal: a condition must be false

scenario: you want to show a login button, but only to users who are not currently authenticated.
operator: negation (not)
logic: NOT is_authenticated
outcome: the expression is True only when is_authenticated is False.

goal: two states must be identical

scenario: you are verifying data integrity. a record is considered valid only if its is_processed flag has the same value as its is_archived flag.
operator: biconditional (iff)
logic: is_processed IFF is_archived
outcome: the expression is True if both flags are True or if both flags are False.

goal: a specific condition guarantees an outcome

scenario: you have a system rule: if a user has more than 100 points, they must be a “gold” member.
operator: implication (if…then)
logic: has_100_points IMPLIES is_gold_member
outcome: this rule is only violated (evaluates to False) if a user has 100+ points but is not a gold member. if they have fewer than 100 points, the rule holds true regardless of their status.