When simplifying a Boolean function on a Karnaugh map, the essential prime implicant must be included because it covers a 1 that no other prime implicant covers.

When minimizing the Boolean function, we found three essential prime implicants that cover minterms no other implicant covers.

Researchers studying the implicational propositional calculus have explored which axioms suffice to derive all tautologies expressible with implication and false.

When minimizing the Boolean function, I decided to remove the non-essential prime implicants to simplify the cover.

On the Karnaugh map, a non-essential prime implicant can be removed without affecting the function because every 1 it covers is also covered by another prime implicant.