# Boolean AND

In a decision table, a rule with AND’ed Conditions is expressed as a single column, with values for each Condition aligned vertically in that column. For example:
In this scenario, each Condition has a set of 2 possible values:
person is 45 or older:   {true, false}
person is a smoker:   {true, false}
and the outcome may also have two possible values:
person’s risk rating:   {low, high}
These Conditions and Actions yield the following truth table:
 age >= 45 smoker risk rating true true high true false false true false false
Note that we have only filled in a single value of risk rating, because the business rule above only covers a single scenario: where age >= 45 and smoker = true. A Completeness Check quickly identifies the remaining 3 scenarios:
Completing the truth table and the Rulesheet requires the definition of 2 additional business rules:
and updating the truth table, we recognize the classic AND Boolean function.
 age >= 45 smoker risk rating true true high true false low false true low false false low
Once the basic truth table framework has been established in the Rulesheet by the Completeness Checker – in other words, all logical combinations of Conditions have been explicitly entered as separate columns in the Rulesheet – we can alter the outcomes to implement other standard Boolean constructions. For example, the NAND construction has the following truth table: