Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is

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

The contrapositive of the statement "If you are born in India,then you are a citizen of India" is:

Check whether the following statement is true or false by proving its contrapositive: If $x, y \in \mathbb{Z}$ such that $xy$ is odd,then both $x$ and $y$ are odd.

If the Boolean expression $(p \wedge q) \circledast (p \otimes q)$ is a tautology,then $\circledast$ and $\otimes$ are respectively given by

Consider statements $p: S_1$ is closed; $q: S_2$ is closed; $r: S_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively.