Which Venn diagram represent the truth of the statement“No policeman is a thief”

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?

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

The negation of the statement

''If I become a teacher, then I will open a school'', is

Which statement given below is tautology ?

Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements

$(i)$ $p \leftrightarrow  q$ 

$(ii)$ $~ p \leftrightarrow q$

$(iii)$ $~ q \leftrightarrow p$

$(iv)$ $~ p \leftrightarrow ~ q$