Question

Упростить логическое выражение

Answer 1

$displaystyle 1. (overline{alor b}to c)equivoverline{overline blor a}=(overline{a+b}to c)equivoverline{overline b+a}= \ (a+b+c)equiv overline ab=(a+b+c)overline ab+overline{a+b+c}cdotoverline{overline ab}= \ 0+overline ab+overline abc+overline{a+b+c+overline ab}=overline ab(1+c)+overline{a+c+b(1+overline a)}= \ overline ab+overline{a+b+c}=overline ab+overline aoverline boverline c=overline a(b+overline boverline c)=overline a(b+overline c)$

$displaystyle 2. ((overline{ato b})tooverline{clor a})equivoverline b=((ato b)+overline{c+a)})equivoverline b= \ (overline a+b+overline ccdotoverline a)equivoverline b=(overline a(1+overline c)+b)equivoverline b=overline a+bequivoverline b= \ (overline a+b)overline b+overline{overline a+b}cdot b=overline aoverline b+0+aoverline bb=overline aoverline b$