0

Suppose I have a theorem's statement as follows:

If statement A and statement B, then statement C.

I want to prove the converse, but quite confused what conditions to consider. I got hint as follows:

  1. Given statement C and statement A, then prove statement B

                 OR

  2. Given statement C and statement B, then prove statement A.

Can anybody help me in this. thanks for your help.

monalisa
  • 4,460

1 Answers1

2

The statement you have is $$A \wedge B \implies C$$

The converse is simply $C \implies A \wedge B$. So to prove the converse, assume $C$ and prove $A$. Then assume $C$ and prove $B$. Then you're done.

  • I have one doubt. When I assume C and then try to prove A, is there any role of B? should i drop that condition while assuming C and proving A? kindly clear this doubt. thanks – monalisa Jan 02 '14 at 04:52
  • 1
    @monalisa It might be the case that the proof $C \implies B$ is useful in the proof that $C \implies A$, or that the two facts are related somehow. Or if you've shown that $C \implies B$, you can assume both $B$ and $C$ in proving $A$. But whether this is useful depends on the details of the propositions. –  Jan 02 '14 at 04:53
  • ok. thanks a lot for your help :) – monalisa Jan 02 '14 at 04:59