Question 483383
the statement is:
if i am hungry then i will eat
the inverse of that statement is:
if i am not hungry then i will not eat.
the converse of that statement is:
if i will eat, then i am hungry.
the contra-positive of that statement is:
if i do not eat, then i am not hungry.


we can translate those statements into logic symbols and variables.


we let p = i am hungry
we let q = i will eat


if i am hungry then i will eat translates to p->q
if i am not hungry then i will not eat translates to ~p->~q
if i eat, then i am hungry translates to q->p
if i don't eat, then i am not hungry translates to ~q->~p


the general rule is:
p->q is the statement.
~p->~q is the inverse.
q->p is the converse.
~q->~p is the contra-positive.


the statement and the contra-positive are equivalent.  if the statement is true, then the contra-positive is also true.
the inverse and the converse are equivalent.  if the inverse is true, then the converse is also true.


the statement and the converse are not equivalent.  sometimes the converse is true when the statement is true and sometimes it's not.
the statement and the inverse are not equivalent.   sometimes the inverse is true when the statement is true and sometimes it's not.


the original statement is:
if i am hungry then i will eat
the statement you are asked to analyze is:
if i am not hungry then i will not eat.
that's the inverse of the statement and it is not true by the fallacy of the inverse.