Why are products called minterms and sums called maxterms?

Question

Do they have a reason for doing so? I mean, in the sum of minterms, you look for the terms with the output 1; I don\'t get why they call it \"minterms.\" Why not maxterms becaus

Answer 1

Here is another way to think about it.

A product is called a minterm because it has minimum-satisfiability where as a sum is called a maxterm because it has maximum-satisfiability among all practically interesting boolean functions.

They are called terms because they are used as the building-blocks of various canonical representations of arbitrary boolean functions.

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Details:

Note that '0' and '1' are the trivial boolean functions. Assume a set of boolean variables x1,x2,...,xk and a non-trivial boolean function f(x1,x2,...,xk).

Conventionally, an input is said to satisfy the boolean function f, whenever f holds a value of 1 for that input.

Note that there are exactly 2^k inputs possible, and any non-trivial boolean-function can satisfy a minimum of 1 input to a maximum of 2^k -1 inputs.

Now consider the two simple boolean functions of interest: sum of all variables S, and product of all variables P (variables may/may-not appear as complements). S is one boolean function that has maximum-satisfiability hence called as maxterm, where as P is the one having minimum-satisfiability hence called a minterm.