# Maxterm: misinformation or different approach to understanding

I have found myself in a crossway of two different explanations regarding Boolean algebra, Maxterm. However, I cannot grasp, whether there is a trick to it or whether one of explanations is an actual misinformation.

Here is a truth table for Minterms and Maxterms (table was found by searching it though the web):

This is another truth table for Maxterms only, however the order of indexes ($$\M_0,..., M_7 \$$) is exactly opposite from the table above (this table was provided by my university professor):

As I asked him for explanation, he answered that in the end, order of indexes doesn't matter, as long as it is true, that DeMorgan theorem applies to Minterms and Maxterms.

However I don't understand the relation between Minterms and Maxterms regarding DeMorgan's theorem.

The problem occurs when one asks for sum-of-products regarding a logic function given in a Maxterm form. For example, a function $$f(x_1,x_2,x_3)=\prod M(1, 3, 6)$$ could be written as (regarding upper truth table)

$$f(x_1,x_2,x_3) = (x_1+x_2+\bar x_3)\cdot(x_1+\bar x_2+\bar x_3)\cdot(\bar x_1+\bar x_2+x_3)$$

but could also be written as (regarding lower truth table)

$$f(x_1,x_2,x_3) = (\bar x_1+\bar x_2+ x_3)\cdot(\bar x_1+x_2+x_3)\cdot(x_1+x_2+\bar x_3)$$

If I am not mistaken, only one of logic functions given in sum-of-product form, is correct. Here lies the confusion I cannot explain myself and would like to hear, what others think about this matter. If possible, one could explain it though Boolean algebraic expression.

Indeed, the ordering of indices doesn't matter in that $$ΠM(1,3,6) = Σm(1,3,6)$$ holds both for the straight and for the reversed orders of indexing, providing these are identical on the left and on the right of the equality sign.
The value of $$f(x_1, x_2, x_3)$$ does depend on the index ordering.