Rewrite the following statement in the form "$p$ if and only if $q$":
For you to get an $A$ grade,it is necessary and sufficient that you do all the homework regularly.

The negation of $(p$ $\Rightarrow q)$ $\Rightarrow (q$ $\Rightarrow p)$ is

Let $p$ be the statement '$x$ is an irrational number',$q$ be the statement '$y$ is a transcendental number',and $r$ be the statement '$x$ is a rational number or $y$ is a transcendental number'.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.

Consider the following statements.
$p$: If $3^4 > 4^3$, then $3^3 > 4^4$
$q$: The roots of the equation $x^2 - 2x + 2 = 0$ are real if and only if Mumbai is in Maharashtra.
$r$: Statement $p$ is true or statement $q$ is false.
Which of the following has truth value $T$ (true)?

The symbolic form of the following circuit is (where $p, q$ and $r$ represent switches $s_{1}, s_{2}$ and $s_{3}$ which are closed respectively):

The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic." is