Proving Biconditionals Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

To start practicing proofs of biconditional (i.e., “if and only if”) statements, think about how you would prove that for all integers n, n is odd if and only if n+1 is even. For instance, what are the two conditionals that this breaks down into? How would you prove them? Our textbook talks about proving biconditionals by proving each of their component conditionals separately, but can you think of other ways to do it?