# Consider this statement "If the bank was robbed then I will not have any money".

Therefore, given $\textbf{p}$: "The bank was robbed" and $\textbf{q}$: "I will not have any money", which of the following are correct?

(1) The converse is $\sim p \rightarrow q$

(2) The inverse is $\sim q \rightarrow p$

(3) The contrapositive is $q \rightarrow \sim p$

(A) (1), (2) and (3) are all incorrect (B) (1) and (2) are correct, (3) is incorrect (C) (1), (2) and (3) are all correct (D) Only (3) is correct

Given this statement "If the bank was robbed then I will not have any money", where $\textbf{p}$: "The bank was robbed" and $\textbf{q}$: "I will not have any money",
The converse is "If I do not have money, then the bank was robbed" $\Rightarrow \sim q \rightarrow p$
The inverse is "If the bank was not robbed, then I have money" $\Rightarrow \sim q \rightarrow p$
The contrapositive is "If I have any money, then the bank was robbed" $\Rightarrow q \rightarrow \sim p$
Therefore (1) and (2) are incorrect and (3) is correct $\rightarrow$ (D) is the correct answer.