implicant

let $\text{[math]}$ denote the variables of a boolean function $\text{[math]}$ , an implicant of $\text{[math]}$ is a product $\text{[math]}$ , $\text{[math]}$ , of a subset of the literals of $\text{[math]}$ (the variables and their complements) such that if $\text{[math]}$ , then $\text{[math]}$ . (this is denoted $\text{[math]}$ .) the set of implicants of a function $\text{[math]}$ is denoted $\text{[math]}$ .
[cite:;taken from @computation_savage_1998 definition 9.6.1]

an implicant $\text{[math]}$ of a boolean function $\text{[math]}$ is a prime implicant if there is no implicant $\text{[math]}$ different from $\text{[math]}$ such that $\text{[math]}$ . the set of prime implicants of a function $\text{[math]}$ is denoted $\text{[math]}$ .
[cite:;taken from @computation_savage_1998 definition 9.6.1]

a monotone implicant (also called monom) of a monotone boolean function $\text{[math]}$ is the product ( $\text{[math]}$ ) $\text{[math]}$ of uncomplemented variables of $\text{[math]}$ such that if $\text{[math]}$ on input $\text{[math]}$ -tuple $\text{[math]}$ , then $\text{[math]}$ . the empty monom has value 1. the set of monotone implicants of a function $\text{[math]}$ is denoted $\text{[math]}$ .
[cite:;taken from @computation_savage_1998 definition 9.6.1]

a monotone implicant $\text{[math]}$ of a boolean function $\text{[math]}$ is a monotone prime implicant if there is no monotone implicant $\text{[math]}$ different from $\text{[math]}$ such that $\text{[math]}$ . the set of monotone prime implicants of a function $\text{[math]}$ is denoted $\text{[math]}$ .
[cite:;taken from @computation_savage_1998 definition 9.6.1]