Question:
Let $A$, $B$, and $C$ represent statements, and let $p(A)$, $p(B)$, and $p(C)$ be their truth values. Find all compound statements that are true (i.e., have a truth value of $1$) for the given truth values of $A$, $B$, and $C$.
Project ID:
7400120171
Answer 1:
$$
\begin{gather}
p(A)=1,~p(B)=1, \cr
A \vee \neg B
\end{gather}
$$
Answer 1 Correct:
1
Answer 2:
$$
\begin{gather}
p(A)=1,~p(B)=0, \cr
A \wedge \neg B
\end{gather}
$$
Answer 2 Correct:
1
Answer 3:
$$
\begin{gather}
p(A)=1,~p(B)=1,~p(C)=0, \cr
A \Rightarrow (B \wedge \neg C)
\end{gather}
$$
Answer 3 Correct:
1
Answer 4:
$$
\begin{gather}
p(A)=1,~p(B)=1,~p(C)=1, \cr
\neg (A \vee C) \Rightarrow B
\end{gather}
$$
Answer 4 Correct:
1
Answer 5:
$$
\begin{gather}
p(A)=1,~p(B)=1,~p(C)=1, \cr
(\neg A \wedge B) \Rightarrow C
\end{gather}
$$
Answer 5 Correct:
1
Answer 6:
$$
\begin{gather}
p(A)=0,~p(B)=0, \cr
\neg A \Leftrightarrow B
\end{gather}
$$
Answer 6 Correct:
0
Answer 7:
$$
\begin{gather}
p(A)=1,~p(B)=1,~p(C)=0, \cr
(A \wedge B) \vee\neg C
\end{gather}
$$
Answer 7 Correct:
1
Answer 8:
$$ \begin{gather} p(A)=0,~p(B)=0,\cr \neg A \Rightarrow B \end{gather} $$
Answer 8 Correct:
0