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Implicant :

A normal product term that implies Y.

Example: For the function Y = AB + ABC + BC, the implicants are AB, ABC, and BC because if any one of those terms are true, then Y is true.

Prime Implicant :

An implicant of Y such that if any variable is removed from the implicant, the resulting term does not imply Y.

Example: Y = AB + ABC + BC
Prime Implicants: AB, BC

Not a prime implicant: ABC

ABC is not a prime implicant because the literal A can be removed to give BC and BC still implies Y. Conversely AB is not a prime implicant because you can't remove either A or B and have the remaining term still imply Y.

In truth tables the prime implicants are represented by the largest rectangular groups of ones that can be circled. If a smaller subgroup is circled, the smaller group is an implicant, but not a prime implicant.

Minterm:

Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. These concepts are dual because of their complementary-symmetry relationship as expressed by De Morgan's laws.

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