(a <=> b) <=/=> [(b => TRUE) <=> a]

This is a critique of honor societies which do not serve a point in proving someone’s “honor”. The college requirement is essentially: Join this club to prove you have joined this club. Anyone can join an “honor” society without demonstrating anything related to honor, meaning:

([Joining an honor society] => TRUE) <=> [Being allowed to join college]

Being allowed to drive a car implies having a license and having a license implies being allowed to drive a car. Neither of these implies TRUE - in an ideal world at least.

By the way, TRUE is a tautology because it is always true, which is the definition of a tautology. Unnecessary repetition is not a requirement of a tautology.