"Richmond will win the AFL premiership only if pigs can fly"
Here is how ive gone about doing this:
if p="pigs can fly" and r="Richmond will win the AFL premiership"
then the above statement can be written as p-->r
converse: (-p)-->(-r) If pigs can't fly, Richmond will not win the AFL premiership.
contrapositive: (-r)-->(-p) If Richmond do not win the AFL premiership then pigs cannot fly
Is what I have done correct? The answers given suggest otherwise, but I'm convinced that I haven't made a mistake. Can anyone clarify this?
I would like to add that AFAIK the converse of p -> r is r -> p, while ~p -> ~r is the contrapositive of the converse. Now, the contrapositive of any statement q is equivalent to q, so whether to consider r -> p or ~p -> ~r the converse of p -> r is a matter of nomenclature rather than logical equivalence.