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Possible way to "Brake" Boole's truth table. Need help

Well Following this thread: http://mathhelpforum.com/algebra/201...-question.html (Which was missplaced), i want to ask another question.

So lets say that we have 3 digital inputs X, Y, Z and 1 digital output Q. The truth table for this output is :

Attachment 24355

"Breaking" this truth table into 2 other truth tables with 2 inputs each is not always possible. But how about breaking it

into 3 truth tables (well not exactly 3, more like 2 full and 2 half ones).

Well i think that the way to do it is shown below:

Attachment 24357

As you can see we use 2 "virtual" outputs representedby lower case letters a,b and we create 2 "complete" truth tables following the output patern of the original table.

Then we use these "virtual" outputs to create other 2 "half" truth tables where the Input X is "0" in the first and "1" in the second and the output Q is the same as

the inputs a and b, "0" and "1" in each table.

Do you think that this method is correct ?

Thanks in advance.