The statement $p \rightarrow (q \rightarrow p)$ is equivalent to
$p \rightarrow (p \rightarrow q)$
$p \rightarrow (q\, \vee \, p)$
$p \rightarrow (q\, \wedge p)$
$p \rightarrow (p \leftrightarrow q)$
The negation of the statement
''If I become a teacher, then I will open a school'', is
The contrapositive of the statement "I go to school if it does not rain" is
The statement $\sim[p \vee(\sim(p \wedge q))]$ is equivalent to
Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(\sim p) \Rightarrow(p \wedge q) \vee r \quad$ is a tautology. Then ' $r$ ' is equal to
The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is