Negation of the statement $(p \vee r) \Rightarrow (q \vee r)$ is :

The dual of the statement pattern $\sim p \wedge (q \vee t)$ is (where $t$ is a tautology and $c$ is a contradiction).

If $(p \wedge \sim q) \wedge r \to \sim r$ is $F$,then the truth value of $r$ is:

Consider the following three statements:
$(A)$ If $3+3=7$ then $4+3=8$.
$(B)$ If $5+3=8$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$.
Which of the following statements is correct?

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 $(p \Leftrightarrow \sim q)$.

If $p:$ Seema is fat. $q:$ She is happy,then the logical equivalent statement of 'If Seema is fat,then she is happy' is