Given the phrase "Where NONE of the following are TRUE" and two statements how should a boolean logic be composed? Let's have two statements


(value > 10)
(value &lt; 25)


And a list of items with the following values


10
20
30


This is what a truth table would give

Item  Value  (value &gt; 10)  (value &lt; 25)
----  -----  ------------  ------------
1     10     FALSE         TRUE
2     20     TRUE          TRUE
3     30     TRUE          FALSE


Example 1

Where ALL of the following are TRUE
   value &gt; 10
   value &lt; 25


This one is easy and we get the following

Where (value &gt; 10) AND (value &lt; 25)


The result is then a single value of 20

Example 2

Where NONE of the following are TRUE
   value &gt; 10
   value &lt; 25


This is where I am not sure of what to generate.

This would be "simple" as it is only a NOT of the whole expression

Where NOT ((value &gt; 10) AND (value &lt; 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 &gt; 10) OR (value &lt; 25))


And the result would be that no items are produced.

What is the correct meaning of NONE here?
The correct meaning is: 

"Where (NOT (value > 10)) AND (NOT (value &lt; 25))".

Applying one of the De Morgan's laws: 

1) P AND Q &lt;=> NOT( (NOT P) OR (NOT Q) )
2) P OR Q &lt;=> NOT( (NOT P) AND (NOT Q) )

we get: 

"Where NOT ( (NOT(NOT(value > 10))) OR (NOT(NOT(value &lt; 25))) )"

and the equivalent final result is

"Where NOT ((value > 10) OR (value &lt; 25))" :-)