# Thread: Elementary Number Theory - when to use converse?

1. ## Elementary Number Theory - when to use converse?

ok - test it like 2 hours and only one thing I'm ucertain of:
when would you use converse?? I understand contrapositive can be used to prove if Q part is easier to work with and all that - but I still don't understand when you would need to use converse??

2. Hello,
Originally Posted by cassiopeia1289
ok - test it like 2 hours and only one thing I'm ucertain of:
when would you use converse?? I understand contrapositive can be used to prove if Q part is easier to work with and all that - but I still don't understand when you would need to use converse??
Remember that the converse of an implication $A \Longrightarrow B$ is $B \Longrightarrow A$

The converse can be used of course to prove equivalences, since $A \Longleftrightarrow B$ is $(A \Longrightarrow B) \wedge (B \Longrightarrow A)$

Here are two links talking about some uses of the converse :
Converse, Inverse, Contrapositive
Logic - Converse

If you look at the second link, you can see that there's no direct relation between the truth table of the implication and the one of the converse.

Right now, I can't remember using the converse to prove anything... Maybe I did...