How can we simplify $$F=MNO+Q'P'N'+PRM+Q'OMP'+MR$$ using the theorems of boolean algebra, not Karnaugh or anything else?
Well, I can obviously simplify $MR(P+1)=MR$, so the expression becomes $$MNO+Q'P'N'+MR+Q'OMP'$$ But from here, I tried to use De Morgan or to calculate the negative form of $F$, but none of this helps.
$$\begin{align*} F&=MNO+Q′P′N′+PRM+Q′OMP′+MR\\ &=MNO+Q′P′N′+Q′OMP′+MR(P+1)\\ &=MNO+Q′P′N′+Q′OMP′+MR\\ &=MNO+MR+Q'P'N'+Q'OMP'\\ &=MNO+MR+Q'P'N'+(Q'P'N')'Q'OMP'\\ &=MNO+MR+Q'P'N'+(Q+P+N)Q'OMP'\\ &=MNO+MR+Q'P'N'+NQ'OMP'\\ &=MNO(1+Q'P')+MR+Q'P'N'\\ &=MNO+MR+Q'P'N' \end{align*}$$