Let $a : \sim (p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false,then the truth values of $a$ and $b$ are respectively:

Let $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta ((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to

Let $p$ and $q$ stand for the statements "$2 \times 4 = 8$" and "$4$ divides $7$" respectively. Then the truth values of the following biconditional statements are:
$(i)$ $p \leftrightarrow q$
$(ii)$ $\sim p \leftrightarrow q$
$(iii)$ $\sim q \leftrightarrow p$
$(iv)$ $\sim p \leftrightarrow \sim q$

The correct logical equivalences from the following are: $(I)$ $p \to (q \to r) \equiv (p \land q) \to r$ $(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$ $(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$ $(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$

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

Identify the quantifier in the following statement and write the negation of the statement.
There exists a capital for every state in India.