Inverse, Converse and contraposition of statement? I am trying to break the statements:
"Being rich is necessary for Alex to be happy"(1) and "Stop, or I will shoot!"(2)
(1) Statement
$\neg Rich \Rightarrow \neg Happy$
Converse
$\neg Happy \Rightarrow \neg Rich  $
Inverse
$ Rich \Rightarrow  Happy$
Contrapositive
$Happy \Rightarrow Rich  $
(2) Statement
$\neg Stop  \Rightarrow \neg Shot$
Converse
$\neg Shot \Rightarrow  \neg Stop $
Inverse
$ Stop  \Rightarrow  Shot$
Contrapositive
$Shot \Rightarrow   Stop $
Is this true?
I appreciate your answer!
UPDATE
(2) Statement
$\neg Stop  \Rightarrow Shot$
Converse
$ Shot \Rightarrow  \neg Stop $
Inverse
$ Stop  \Rightarrow  \neg Shot$
Contrapositive
$\neg Shot \Rightarrow   Stop $
 A: Your answers to $(1)$ are just fine. You seem to understand the relationships between an implication, its converse, inverse, and its contrapositive.

Implication: $A \equiv (p \rightarrow q)$



*

*converse of $A$: $\;q\rightarrow p$

*inverse of $A$: $\;\lnot p \rightarrow \lnot q$

*contrapositive: $\;\lnot q \rightarrow \lnot p$


Note that $\,A \equiv \text{contrapositive(A)}\;$ and $\;\text{inverse(A)}\equiv \text{converse(A)}$.
$(2)$ Here, your initial translation is incorrect, and as a consequence, so are the  converse, inverse, and contrapositives.
Let's look at $(2)$ again. 

Stop, or I'll shoot $\iff$ If you don't stop, then I'll shoot.

This can be translated into two equivalent logical statements:
$\text{Stop} \lor \text{Shot}\,\equiv \lnot \,\text{Stop}\rightarrow \text{Shot}\tag{2}$
Now, use what you know about the converse of an implication, the inverse, and the contrapositive to write the corresponding statements to the implication given on the right-hand side of $(2)$

UPDATE: Now you're spot on!

