# Thread: To show the function in disjunctive normal form

1. ## To show the function in disjunctive normal form

Hi guys!
Problems with discrete mathematics, really need your help.
I did the truth table:

But can not understand how to make the following points:
• to show the function in disjunctive normal form; - Done
• to show the function as a polynomial Zhegalkin; - Done
• Minimize the basis of DNF; - Done
show the minimum function in the bases Schaeffer and Pierce

There is nothing difficult in writing functions in the bases of Sheffer and Pierce, but the results are probably going to be too long. For Sheffer stroke | (NAND) we have $\neg P=P\mid P$, $P\land Q=(P\mid Q)\mid(P\mid Q)$ and $P\lor Q=(P\mid P)\mid(Q\mid Q)$. For Peirce arrow $\downarrow$ (NOR) we have $\neg P=P\downarrow P$, $P\land Q=(P\downarrow P)\downarrow(Q\downarrow Q)$ and $P\lor Q=(P\downarrow Q)\downarrow(P\downarrow Q)$. You see that formulas occur two times in the translation. I would write a program in some language that can handle inductive datatypes (such as ML or Scheme) to convert formulas to Sheffer and Pierce bases.