The logical statement $(p$ $\rightarrow q) \wedge (p$ $\rightarrow \sim p)$ is equivalent to

If $\sim p \to q$ is false and $q \leftrightarrow r$ is false, then the truth value of $(p, q, r)$ is...

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

Let $S$ be a non-empty subset of $R$. Consider the statement $p : x \in S$ is a rational number such that $x > 0$. Which of the following is the negation of $p$?

The contrapositive of the statement "if $I$ am not feeling well,then $I$ will go to the doctor" is

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