Meaning of an And Phrase followed by an Or Phrase

A sentence begins like "If A and B or C then …" does that mean that A must always be true and one of B or C must be true for the following to happen? Or can just C be true? In programming or math you could put parenthesis around the phrases to clarify your meaning. You could write "If A and (B or C), then…". The reason I ask, is the 25th Amendment of the US Constitution reads:

Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide,