I need a simple example of proving a TONCAS.

Question

I know the definition of the acronym is "The Obvious and Necessary Condition Are Sufficient". I am not exactly clear as to what it means to prove a theorem's TONCAS. Does it simply mean prove the converse since the necessary condition must be also sufficient?

Answer 1

An example of TONCAS is the following proposition:

A graph is a bipartite if and only if it contains no odd cycle.

The "only if" part is obvious and the "if" part is not that obvious. Together this proposition is a TONCAS. You should try to prove these 2 parts seperately to have a feeling about the obviousity.