Mathematical Reasoning

Simplest form of the following switching circuit is

For the circuit show below, the Boolean polynomial is

The statement $\sim(p \leftrightarrow \sim q)$ is

The symbolic form of the following circuit is (where $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ represents switches $\mathrm{s}_{1}, \mathrm{~s}_{2}$ and $\mathrm{s}_{3}$ which are closed respectively)

The statement $[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \mathrm{p}]$ is equivalent to

The stament pattern $\mathrm{p} \rightarrow(\mathrm{q} \rightarrow \mathrm{p})$ is equivalent to

The logical statement $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to

The statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow[(\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{q}]$ is

The statement pattern $\sim(p \leftrightarrow \sim q)$ is

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively

The logical expression $p(\sim p \vee \sim q)=$

The output of the following circuit is