To be consistent, if it were really an illegal dribble, both (a) and (b) would be an illegal dribble since the only difference is between them is the movement of the feet (which is not relevant to the legality of a dribble) and not how the ball was handled.
A player tossing the ball into the air and catching it without it touching anything else is effectively considered to be holding the ball. Thus, it becomes a travel to move the pivot foot during such action.
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