Question

Постройте таблицы истинности для следующих логических выражений

Answer 1

1) $(A rightarrow B) leftrightarrow (A, &,B)$

$begin{center}begin{tabular}{ccccc}A & B & A to B & A & B & F \0 & 0 & 1 & 0 & 0 \0 & 1 & 1 & 0 & 0 \1 & 0 & 0 & 0 & 1 \1 & 1 & 1 & 1 & 1end{tabular}end{center}$

2) $(A to B) to ((A to overline{B}) to overline{A})$

$begin{center}begin{tabular}{cccccccc}A & B & A to B & overline{B} & A to overline{B} & overline{A} & (A to overline{B}) to overline{A} & F \0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 \1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 \1 & 1 & 1 & 0 & 0 & 0 & 1 & 1end{tabular}end{center}$

3) $(A to (C to B)) to (B lor C)$

$begin{center}begin{tabular}{ccccccc}A & B & C & C to B & A to (C to B) & B vee ,C & F \0 & 0 & 0 & 1 & 1 & 0 & 0 \0 & 0 & 1 & 0 & 1 & 1 & 1 \0 & 1 & 0 & 1 & 1 & 1 & 1 \0 & 1 & 1 & 1 & 1 & 1 & 1 \1 & 0 & 0 & 1 & 1 & 0 & 0 \1 & 0 & 1 & 0 & 0 & 1 & 1 \1 & 1 & 0 & 1 & 1 & 1 & 1 \1 & 1 & 1 & 1 & 1 & 1 & 1end{tabular}end{center}$