Conversely means looked at the other way round. Conversely, the poor pay more, and conversely, conversely it may help.
It signals a genuine reversal rather than a mere contrast, which is why using it for a simple however is a common fault. In logic the converse of a statement swaps its two halves and need not be true at all.
1adverbconverselyLooked at the other way round.
“If prices rise, sales usually fall; conversely, if prices fall, sales rise.”
conversely is a connector.
From converse + -ly.
Etymology from Wiktionary, CC BY-SA