Mathematical Reasoning

$\sim p \wedge q$ is logically equivalent to

Identify the false statement?

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

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

If p : switch $\mathrm{s}_1$ is closed, q : switch $\mathrm{s}_2$ is closed then correct interpretation from the following circuit is

The minimum number of switches in the simplified form of the following switching circuit is

If p : switch $\mathrm{S}_1$ is closed, q : switch $\mathrm{S}_2$ is closed, r : switch $\mathrm{S}_3$ closed, then the symbolic form of the following switching circuit is equivalent to Switching Circuit :

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

Which of the following are pairs of equivalent circuits

Which one of the following is the pair of equivalent circuits? i. ii. iii. iv. v?

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

If the statement $p \vee \sim(q \wedge r)$ is false; then the truth values of $p, q$ and $r$ are respectively