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:

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.  Running The completeness checker as described in the Rule Modeling section quickly identifies the remaining three 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.

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: