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Art of Computer Programming, Volume 4A, The: Combinatorial Algorithms, Part 1 by Donald E. Knuth

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The terms of a DNF are often called implicants, because the truth of any term in a disjunction implies the truth of the whole formula. In a formula like

Image

for example, we know that f is true when Image is true, namely when (x, y, z) = (1, 0, 1). But notice that in this example the shorter term x z also turns out to be an implicant of f, even though not written explicitly, because the additional term y z makes the function true whenever x = z = 1, regardless of the value of y. Similarly, y is an implicant of this particular function. So we might ...

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