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What about the converse?

This is one of my favourite exercises. Actually it’s more of a competition. To emphasize the importance of converse statements I set a simple challenge for my students. In a different lecturer’s class (i.e., not in mine) all they have to do is ask the question “What about the converse?” when a statement of the form A\implies B is used. Nothing more. (The statement can be in any format, e.g. “If …, then …”). The first person to do that wins a prize: one of chocolates, wine or a signed photograph of me. (Rather unbelievably, the latter has been claimed more than once.)

The reasoning behind this is to send a message. Even if students, at the moment the challenge is set, do not really understand what a converse is, or that it might not be true even if the original statement is, they know that I think the concept is important and that is enough to make them pay attention to it.

Usually, I tell the students they should all applaud when someone asks the question. That perplexes other lecturers when that first happens and so far I haven’t got in to trouble with my colleagues. They take the minor disruption in the spirit it is intended.

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