Let's have two statements(value > 10)(value < 25)And a list of items with the following values102030This is what a truth table would giveItem  Value  (value > 10)  (value < 25)----  -----  ------------  ------------1     10     FALSE         TRUE2     20     TRUE          TRUE3     30     TRUE          FALSEExample 1Where ALL of the following are TRUE   value > 10   value < 25This one is easy and we get the followingWhere (value > 10) AND (value < 25)The result is then a single value of 20Example 2Where NONE of the following are TRUE   value > 10   value < 25This is where I am not sure of what to generate.This would be simple as it is only a NOT of the whole expressionWhere NOT ((value > 10) AND (value < 25))However, the result is then two values (10 and 30)From what someone would think of NONE of the two statements would be something like:Where NOT ((value > 10) OR (value < 25))And the result would be that no items are produced.What is the correct meaning of NONE here?
Given the phrase Where NONE of the following are TRUE and two statements how should a boolean logic be composed?
logic
The correct meaning is: Where (NOT (value > 10)) AND (NOT (value < 25)).Applying one of the De Morgan's laws: 1) P AND Q <=> NOT( (NOT P) OR (NOT Q) )2) P OR Q <=> NOT( (NOT P) AND (NOT Q) )we get: Where NOT ( (NOT(NOT(value > 10))) OR (NOT(NOT(value < 25))) )and the equivalent final result isWhere NOT ((value > 10) OR (value < 25)) :-)