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

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.

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.