minterm in 
BooleanMinterms
BooleanMinterms[k,n]
represents the k
minterm in n variables.
BooleanMinterms[{k1,k2,…},n]
represents the disjunction of the minterms ki.
BooleanMinterms[{{u1,…,un},{v1,…},…}]
represents the disjunction of minterms given by the exponent vectors ui, vi, ….
BooleanMinterms[spec,{a1,a2,…}]
gives the Boolean expression in variables ai corresponding to the minterms function specified by spec.
BooleanMinterms[spec,{a1,a2,…},form]
gives the Boolean expression in the form specified by form.
Details
- BooleanMinterms[{{u1,u2,…}},{a1,a2,…}] gives b1∧b2∧… where bi==ai if ui is True and bi=¬ai if ui is False.
- The ui etc. can be either True and False or 1 and 0.
- BooleanMinterms[k,n] is equivalent to BooleanMinterms[{IntegerDigits[k,n,2]}].
- BooleanMinterms[spec] gives a Boolean function object that works like Function.
- BooleanMinterms[spec][a1,a2,…] gives an implicit representation equivalent to the explicit Boolean expression BooleanMinterms[spec,{a1,a2,…}].
- BooleanConvert converts BooleanMinterms[spec][vars] to an explicit Boolean expression.
- In BooleanMinterms[spec,{a1,a2,…},form], the possible forms are as given for BooleanConvert.
- BooleanMinterms[spec,{a1,a2,…}] by default gives an expression in DNF.
Examples
open all close allBasic Examples (4)
Equivalent ways of specifying the same minterm:
BooleanMinterms[{{True, False, True}}, {a, b, c}]BooleanMinterms[{{1, 0, 1}}, {a, b, c}]BooleanMinterms[{5}, {a, b, c}]Specify a disjunction of minterms:
BooleanMinterms[{1, 3, 5}, {a, b, c}]An equivalent way to specify a disjunction of minterms:
Or@@Table[BooleanMinterms[{i}, {a, b, c}], {i, {1, 3, 5}}]TautologyQ[Equivalent[%%, %]]Return a BooleanFunction object representing the disjunction of minterms:
BooleanMinterms[{1, 3, 5}, 3]@@{a, b, c}BooleanMinterms[{1, 3, 5}, {a, b, c}]TautologyQ[Equivalent[%%, %]]Enumerate all minterms of three variables:
Table[BooleanMinterms[{i}, {a, b, c}], {i, 0, 2 ^ 3 - 1}]Scope (2)
Specify different forms for the result:
BooleanMinterms[{1, 3, 5}, {a, b, c}, "DNF"]BooleanMinterms[{1, 3, 5}, {a, b, c}, "CNF"]BooleanMinterms[{1, 3, 5}, {a, b, c}, "ANF"]Use exponent vectors to specify a conjunction of minterms:
BooleanMinterms[{{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}]BooleanConvert[%[a, b, c], "DNF"]Properties & Relations (4)
The indices correspond to positions of True in the default ordering for BooleanTable:
BooleanTable[BooleanMinterms[{0, 3, 7}, {a, b, c}], {a, b, c}]Length[%] - Position[%, True]BooleanMinterms can represent any BooleanFunction:
f = BooleanMinterms[{1, 5, 7}, 3]g = BooleanFunction[FromDigits[{1, 0, 1, 0, 0, 0, 1, 0}, 2], 3]f === gThe mapping from minterms to index:
mindex[l_, k_] := FromDigits[Table[If[MemberQ[l, i], 1, 0], {i, 2 ^ k - 1, 0, -1}], 2]mindex[{1, 5, 7}, 3]The mapping from index to minterms:
indmin[m_, k_] := Flatten@Position[Reverse[IntegerDigits[m, 2, 2 ^ k]], 1] - 1indmin[162, 3]With[{m = 123, k = 4}, BooleanMinterms[Select[Range[0, 2^k - 1], BitAnd[2^#, m] ≠ 0&], k] === BooleanFunction[m, k]]Use Subsets to enumerate all possible Boolean functions using BooleanMinterms:
BooleanMinterms[#, {a, b}]& /@ Subsets[Range[0, 2 ^ 2 - 1]]BooleanMaxterms is related to BooleanMinterms:
f = BooleanMaxterms[{1, 3, 5}, 3]g = BooleanMinterms[{1, 3, 5}, 3]TautologyQ[Equivalent[f[a, b, c], ¬g[¬a, ¬b, ¬c]]]Text
Wolfram Research (2008), BooleanMinterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMinterms.html.
CMS
Wolfram Language. 2008. "BooleanMinterms." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanMinterms.html.
APA
Wolfram Language. (2008). BooleanMinterms. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanMinterms.html