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\begin{Example} In Exercise \ref{XorIsNice} we observed that the operator $\OR$ corresponds to neither the sum in $\Fb$ nor the multiplication in $\Fb$. We would like to define a Boolean function   $$o: (\Fb)^2 \rightarrow \Fb, \Fb,\,  o \in \Fb[x,y]$$   $$(x,y) \Fb[x,y],\, (x,y)  \mapsto o(x,y), $$ o(x,y),$$  that corresponds to the $\OR$ operator. We need the De Morgan law, which is used in logic:  \[  \NOT(x\, \OR \, y)=\NOT(x)\, \AND\, \NOT(y) 
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\[  o(x,y)=\big((x+1)(y+1)\big)+1,  \]  which is after simplifications (after simplifications)  \[  o(x,y)=xy+x+y.  \]