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Решебник по алгебре 8 класс Мерзляк Упражнения (страница 210)

Авторы:
Год:2023
Тип:учебник
Серия:Алгоритм успеха

Упражнения (Страница 210)

\[\boxed{\mathbf{Упражнения}\mathbf{\ }\mathbf{стр}\mathbf{.\ 210}}\]

\[\boxed{\mathbf{1.}}\]

\[Являются\ высказываниями:\]

\[1,\ 4,\ 6.\]

\[Не\ являются\ высказываниями:\ \ \]

\[2,\ 3,\ 5,\ 7.\]

\[\boxed{\mathbf{2.}}\]

\[A = \left\{ 5 < 6 \right\};\ \ \ \]

\[B = \left\{ 6 - простое\ число \right\}\]

\[1)\ ложное;\]

\[2)\ истинное;\]

\[3)\ ложное;\]

\[4)\ ложное;\]

\[5)\ ложное;\]

\[6)\ истинное.\]

\[\boxed{\mathbf{3.}}\]

\[1)\ \overline{A} \Longrightarrow B\]

\[A\] \[\overline{A}\] \[B\] \[\overline{A} \Longrightarrow B\]
\[1\] \[0\] \[1\] \[0\]
\[0\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[0\] \[1\]
\[0\] \[1\] \[0\] \[1\]

\[2)\ (A \vee B) \land C\]

\[A\] \[B\] \[C\] \[A \vee B\] \[(A \vee B) \land C\]
\[1\] \[1\] \[1\] \[1\] \[1\]
\[1\] \[1\] \[0\] \[1\] \[0\]
\[1\] \[0\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[0\] \[1\] \[0\]
\[0\] \[1\] \[1\] \[1\] \[1\]
\[0\] \[1\] \[0\] \[1\] \[0\]
\[0\] \[0\] \[1\] \[1\] \[1\]
\[0\] \[0\] \[0\] \[0\] \[0\]

\[3)\ (A \land B) \Longrightarrow C\]

\[A\] \[B\] \[C\] \[A \land B\] \[(A \land B) \Longrightarrow C\]
\[1\] \[1\] \[1\] \[1\] \[1\]
\[1\] \[1\] \[0\] \[1\] \[0\]
\[1\] \[0\] \[1\] \[0\] \[1\]
\[1\] \[0\] \[0\] \[0\] \[1\]
\[0\] \[1\] \[1\] \[0\] \[1\]
\[0\] \[1\] \[0\] \[0\] \[1\]
\[0\] \[0\] \[1\] \[0\] \[1\]
\[0\] \[0\] \[0\] \[0\] \[1\]

\[4)\ (A \Longrightarrow B) \land (B \vee C)\]

\[A\] \[B\] \[C\] \[A \Longrightarrow B\] \[B \vee C\] \[(A \Longrightarrow B) \land (B \vee C)\]
\[1\] \[1\] \[1\] \[1\] \[1\] \[1\]
\[1\] \[1\] \[0\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[1\] \[0\] \[1\] \[0\]
\[1\] \[0\] \[0\] \[0\] \[0\] \[0\]
\[0\] \[1\] \[1\] \[1\] \[1\] \[1\]
\[0\] \[1\] \[0\] \[1\] \[1\] \[1\]
\[0\] \[0\] \[1\] \[1\] \[1\] \[1\]
\[0\] \[0\] \[0\] \[1\] \[0\] \[0\]

\[5)\ (A \land \overline{C}) \Longrightarrow B\]

\[A\] \[B\] \[C\] \[\overline{C}\] \[A \land \overline{C}\] \[(A \land \overline{C}) \Longrightarrow B\]
\[1\] \[1\] \[1\] \[0\] \[0\] \[1\]
\[1\] \[1\] \[0\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[1\] \[0\] \[0\] \[1\]
\[1\] \[0\] \[0\] \[1\] \[1\] \[0\]
\[0\] \[1\] \[1\] \[0\] \[0\] \[1\]
\[0\] \[1\] \[0\] \[1\] \[0\] \[1\]
\[0\] \[0\] \[1\] \[0\] \[0\] \[1\]
\[0\] \[0\] \[0\] \[1\] \[0\] \[1\]

\[\boxed{\mathbf{4.}}\]

\[1)\ \overline{\overline{A}} = A\]

\[A\] \[\overline{A}\] \[\overline{\overline{A}}\]
\[0\] \[1\] \[0\]
\[1\] \[0\] \[1\]

\[2)\ A \land A = A\]

\[A\] \[A\] \[A \land A\]
\[0\] \[0\] \[0\]
\[1\] \[1\] \[1\]

\[3)\ A \vee B = B \vee A\]

\[A\] \[B\] \[A \vee B\] \[B \vee A\]
\[1\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[1\] \[1\]
\[0\] \[1\] \[1\] \[1\]
\[0\] \[0\] \[0\] \[0\]

\[4)\ A \vee (B \land C) =\]

\[= (A \vee B) \land (A \vee C)\]

\[A\] \[B\] \[C\] \[B \land C\] \[A \vee (B \land C)\]
\[1\] \[1\] \[1\] \[1\] \[1\]
\[1\] \[1\] \[0\] \[0\] \[1\]
\[1\] \[0\] \[1\] \[0\] \[1\]
\[1\] \[0\] \[0\] \[0\] \[1\]
\[0\] \[1\] \[1\] \[1\] \[1\]
\[0\] \[1\] \[0\] \[0\] \[0\]
\[0\] \[0\] \[1\] \[0\] \[0\]
\[0\] \[0\] \[0\] \[0\] \[0\]
\[A\] \[B\] \[C\] \[A \vee B\] \[A \vee C\] \[(A \vee B) \land (A \vee C)\]
\[1\] \[1\] \[1\] \[1\] \[1\] \[1\]
\[1\] \[1\] \[0\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[1\] \[1\] \[1\] \[1\]
\[1\] \[0\] \[0\] \[1\] \[1\] \[1\]
\[0\] \[1\] \[1\] \[1\] \[1\] \[1\]
\[0\] \[1\] \[0\] \[1\] \[0\] \[0\]
\[0\] \[0\] \[1\] \[0\] \[1\] \[0\]
\[0\] \[0\] \[0\] \[0\] \[0\] \[0\]

\[5)\ \overline{A \vee B} = \overline{A} \land \overline{B}\]

\[A\] \[B\] \[A \vee B\] \[\overline{A \vee B}\]
\[1\] \[1\] \[1\] \[0\]
\[1\] \[0\] \[1\] \[0\]
\[0\] \[1\] \[1\] \[0\]
\[0\] \[0\] \[0\] \[1\]
\[A\] \[B\] \[\overline{A}\] \[\overline{B}\] \[\overline{A} \land \overline{B}\]
\[1\] \[1\] \[0\] \[0\] \[0\]
\[1\] \[0\] \[0\] \[1\] \[0\]
\[0\] \[1\] \[1\] \[0\] \[0\]
\[0\] \[0\] \[1\] \[1\] \[1\]

\[6)\ (A \Longrightarrow B) = \overline{B} \Longrightarrow \overline{A}\]

\[A\] \[B\] \[A \Longrightarrow B\]
\[1\] \[1\] \[1\]
\[1\] \[0\] \[0\]
\[0\] \[1\] \[1\]
\[0\] \[0\] \[1\]
\[A\] \[B\] \[\overline{A}\] \[\overline{B}\] \[\overline{B} \Longrightarrow \overline{A}\]
\[1\] \[1\] \[0\] \[0\] \[1\]
\[1\] \[0\] \[0\] \[1\] \[0\]
\[0\] \[1\] \[1\] \[0\] \[1\]
\[0\] \[0\] \[1\] \[1\] \[1\]
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Упражнения (стр. 210)
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